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:

Electroconvulsive Shock Therapy

A mental health treatment that involves triggering seizures in patients through electrical stimulation to alleviate psychological conditions.

Psychosurgery

A medical intervention involving the removal or destruction of brain tissue to treat psychological disorders, notably less common today due to advances in psychiatric medications.

Antipsychotic Drugs

Medications designed to treat psychotic disorders, such as schizophrenia, by altering brain chemistry.

Hallucinations

Perceptions that occur without an external stimulus, involving seeing, hearing, feeling, or smelling something that isn't actually present.

Related Questions

Q12: The conditional distribution of Y given X

Q12: (Requires Appendix material)Discuss how the differences-in-differences estimator

Q12: One of the primary advantages of using

Q16: When the estimated slope coefficient in the

Q28: There has been much debate about the

Q41: When Xt is strictly exogenous,the following estimator(s)of

Q46: The concepts of exogeneity,strict exogeneity,and predeterminedness<br>A)are defined

Q49: There is some evidence that the Phillips

Q50: Indicate for which of the following examples

Q54: Attendance at sports events depends on various