Examlex

Solved

Consider the Multiple Regression Model from Chapter 5,where K =

question 11

Essay

Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold.
(a)Show what the X matrix and the β vector would look like in this case.
(b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here?
(c)You are asked to find the OLS estimator for the intercept and slope in this model using the
formula Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? )
you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now.
(Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? and note that
Yi = Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 0 + Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 1X1i + Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 2X2i + Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? i Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 0 + Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 1 Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 1 + Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 2 Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 2.
Subtracting the second equation from the first,you get
yi = Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 1x1i + Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 2x2i + Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? i)
(d)Show that the slope for the population growth rate is given by Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? 1 = Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? (e)The various sums needed to calculate the OLS estimates are given below: Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = 8.3103; Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = .0122; Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = 0.6422 Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = -0.2304; Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = 1.5676; Consider the multiple regression model from Chapter 5,where k = 2 and the assumptions of the multiple regression model hold. (a)Show what the X matrix and the β vector would look like in this case. (b)Having collected data for 104 countries of the world from the Penn World Tables,you want to estimate the effect of the population growth rate (X1i)and the saving rate (X2i)(average investment share of GDP from 1980 to 1990)on GDP per worker (relative to the U.S. )in 1990.What are your expected signs for the regression coefficient? What is the order of the (X'X)here? (c)You are asked to find the OLS estimator for the intercept and slope in this model using the formula = (X'X)-1 X'Y.Since you are more comfortable in inverting a 2×2 matrix (the inverse of a 2×2 matrix is, = ) you decide to write the multiple regression model in deviations from mean form.Show what the X matrix,the (X'X)matrix,and the X'Y matrix would look like now. (Hint: use small letters to indicate deviations from mean,i.e. ,zi = Zi - and note that Yi = 0 + 1X1i + 2X2i + i = 0 + 1 1 + 2 2. Subtracting the second equation from the first,you get yi = 1x1i + 2x2i + i) (d)Show that the slope for the population growth rate is given by 1 = (e)The various sums needed to calculate the OLS estimates are given below: = 8.3103; = .0122; = 0.6422 = -0.2304; = 1.5676; = -0.0520 Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these. (f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it? = -0.0520
Find the numerical values for the effect of population growth and the saving rate on per capita income and interpret these.
(f)Indicate how you would find the intercept in the above case.Is this coefficient of interest in the interpretation of the determinants of per capita income? If not,then why estimate it?

Definitions:

Down's Syndrome

A genetic disorder caused by the presence of an extra chromosome 21, characterized by developmental delays and distinctive physical features.

Klinefelter Syndrome

A genetic condition in males characterized by the presence of an extra X chromosome, leading to various developmental and physical differences.

Testosterone Replacement Therapy

A medical treatment where testosterone is prescribed to individuals, typically to address issues related to low testosterone levels, such as certain medical conditions or aging.

Phenylketonuria (PKU)

An inherited metabolic disorder characterized by the inability to break down the amino acid phenylalanine, leading to intellectual disability and other health issues if untreated.

Related Questions

Q3: Because statistical software plays such an important

Q4: The formulae for the AIC and the

Q15: Besides maximum likelihood estimation of the logit

Q21: In the Fixed Time Effects regression model,you

Q24: Your textbook gave an example of attempting

Q27: Your textbook derives the OLS estimator as

Q28: In order to use the t-statistic for

Q32: The class of linear conditionally unbiased estimators

Q34: The central limit theorem<br>A)states conditions under which

Q81: When a police officer responds to a