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

question 11

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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:

Syllogism

A form of reasoning in which a conclusion is drawn from two given or assumed propositions (premises), each of which shares a common term not present in the conclusion.

Hallucinogenic Drug

A substance that induces alterations in perception, mood, and thought, often creating experiences that differ from reality.

Middle Term

In a syllogism, the term that appears in both premises but not in the conclusion, serving as a link between the major and minor terms.

Syllogism

A form of logical reasoning where a conclusion is drawn from two given or assumed propositions (premises).

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