Please answer 4.13 to the budget share relation?f. The least squares estimates of In(FOOD) = a₁ + a₂ln(TOTEXP) + e are as follows:ô = 0.2729In(FOOD) = 0.732 +0.608 In(TOTEXP) R² = 0.4019(6.58) (24.91)Interpret the estimated coefficient of In(TOTEXP). Calculate the elasticity in this model at the 5thpercentile and the 75th percentile of total expenditure. Is this a constant elasticity function?g. The residuals from the log-log model in (e) show skewness = -0.887 and kurtosis = 5.023. Carryout the Jarque-Bera test at the 5% level of significance.h. In addition to the information in the previous parts, we multiply the fitted value in part (b) byTOTEXP to obtain a prediction for expenditure on food. The correlation between this value andactual food expenditure is 0.641. Using the model in part (e) we obtain exp [In(FOOD)]. The cor-relation between this value and actual expenditure on food is 0.640. What if any information isprovided by these correlations? Which model would you select for reporting, if you had to chooseonly one? Explain your choice.4.13 The linear regression model is y = B₁ + B₂x+e. Let y be the sample mean of the y-values and theaverage of the x-values. Create variables y = y-y and x = x-x. Letỹ = ax + e.a. Show, algebraically, that the least squares estimator of a is identical to the least square estimatorof B₂. [Hint: See Exercise 2.4.]b. Show, algebraically, that the least squares residuals from y = ax + e are the same as the leastsquares residuals from the original linear model y = B₁ + B₂x + e.4.14 Using data on 5766 primary school children, we estimate two models relating their performance on amath test (MATHSCORE) to their teacher's years of experience (TCHEXPER).Linear relationshipMATHSCORE=478.15 +0.81TCHEXPER R2 = 0.0095 = 47.51(1.19) (0.11)(se)Linear-log relationshipMATHSCORE= 474.25 +5.63 In(TCHEXPER) R2 = 0.0081 = 47.57(se)(1.84) (0.84)a. Using the linear fitted relationship, how many years of additional teaching experience is requiredto increase the expected math score by 10 points? Explain your calculation.b. Does the linear fitted relationship imply that at some point there are diminishing returns to addi-tional years of teaching experience? Explain.c. Using the fitted linear-log model, is the graph of MAa constant rate, at an increasing rate, or at a decreathe fitted linear relationship?d. Using the linear-log fitted relationship,years of extra teaching experience is rExplain your calculation.e. 252 of the teachers had no teaching exptwo models?f. These models have such a low R2 thexpected math score and years of teach4.15 Consider a log-reciprocal model that relatcal of the explanatory variable, In(y) = P₁Exercise 4.17].a. For what values of y is this model defineb. Write the model in exponential form astionship is dy/dx = exp[B, + (B₂/x)]Xag that r0ergaibicXAt7PER increasing atthis compare toce, how manyby 10 s?

Question

Please answer 4.13 to the budget share relation?f. The least squares estimates of In(FOOD) = a₁ + a₂ln(TOTEXP) + e are as follows:ô = 0.2729In(FOOD) = 0.732 +0.608 In(TOTEXP) R² = 0.4019(6.58) (24.91)Interpret the estimated coefficient of In(TOTEXP). Calculate the elasticity in this model at the 5thpercentile and the 75th percentile of total expenditure. Is this a constant elasticity function?g. The residuals from the log-log model in (e) show skewness = -0.887 and kurtosis = 5.023. Carryout the Jarque-Bera test at the 5% level of significance.h. In addition to the information in the previous parts, we multiply the fitted value in part (b) byTOTEXP to obtain a prediction for expenditure on food. The correlation between this value andactual food expenditure is 0.641. Using the model in part (e) we obtain exp [In(FOOD)]. The cor-relation between this value and actual expenditure on food is 0.640. What if any information isprovided by these correlations? Which model would you select for reporting, if you had to chooseonly one? Explain your choice.4.13 The linear regression model is y = B₁ + B₂x+e. Let y be the sample mean of the y-values and theaverage of the x-values. Create variables y = y-y and x = x-x. Letỹ = ax + e.a. Show, algebraically, that the least squares estimator of a is identical to the least square estimatorof B₂. [Hint: See Exercise 2.4.]b. Show, algebraically, that the least squares residuals from y = ax + e are the same as the leastsquares residuals from the original linear model y = B₁ + B₂x + e.4.14 Using data on 5766 primary school children, we estimate two models relating their performance on amath test (MATHSCORE) to their teacher's years of experience (TCHEXPER).Linear relationshipMATHSCORE=478.15 +0.81TCHEXPER R2 = 0.0095 = 47.51(1.19) (0.11)(se)Linear-log relationshipMATHSCORE= 474.25 +5.63 In(TCHEXPER) R2 = 0.0081 = 47.57(se)(1.84) (0.84)a. Using the linear fitted relationship, how many years of additional teaching experience is requiredto increase the expected math score by 10 points? Explain your calculation.b. Does the linear fitted relationship imply that at some point there are diminishing returns to addi-tional years of teaching experience? Explain.c. Using the fitted linear-log model, is the graph of MAa constant rate, at an increasing rate, or at a decreathe fitted linear relationship?d. Using the linear-log fitted relationship,years of extra teaching experience is rExplain your calculation.e. 252 of the teachers had no teaching exptwo models?f. These models have such a low R2 thexpected math score and years of teach4.15 Consider a log-reciprocal model that relatcal of the explanatory variable, In(y) = P₁Exercise 4.17].a. For what values of y is this model defineb. Write the model in exponential form astionship is dy/dx = exp[B, + (B₂/x)]>Xag that r>0ergaibicXAt7PER increasing atthis compare toce, how manyby 10 s?

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