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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:

Spatial Arrangements

The way in which physical space is used and organized to facilitate various activities and processes in an environment, affecting how people interact within it.

Group Norms

Shared expectations and rules that guide the behavior of members within a group or team.

Product Development Teams

Groups of individuals with varied expertise who are tasked with collaborating to develop new products or services for a company.

Team Size

The number of members that constitute a specific team, which can influence the team's dynamics, communication, and effectiveness.

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