Please explain step by step and how you found the answers. I am not understandin

Question

Please explain step by step and how you found the answers. I am not understanding at all... Thanks!

Consider the following dummy variable regression function where food expenditure is a function of disposable income.   

Here Y is food expenditure, X is income and D = 1 if female and D = 0 if male.

A) Using the data set (foodexpenditure.xls) ideestimate the regression function to examine whether food expenditure is different across genders. Interpret your estimated results: explain if food expenditures are different between males and females. Also comment on the statistical significance of your findings. (10)

DATA:

            

B) To allow interactions between X and D estimate the following regression function. (10)

Yi=b1+b2Xi+b3Di+b4(XiDi)+ei

C) Interpret the estimated results you have found in equation. Are the rates of increase in food expenditure due an increase in income are different between males and females? Explain. (10)

Table 6-2 Food Expenditure in Relation to After-Tax Income and Sex Observation Food expenditure (y) After-tax income (x) Dummy Variable (D) DiXi 1 1983 11557 1 11557 2 2987 29387 1 29387 3 2993 31463 1 31463 4 3156 29554 1 29554 5 2706 25137 1 25137 6 2217 14952 1 14952 7 2230 11589 0 0 8 3757 33328 0 0 9 3821 36151 0 0 10 3291 35448 0 0 11 3429 32988 0 0 12 2533 20437 0 0 D=1 if female and D=0 if male

Explanation / Answer

Answer :

Question 1) Interpret your estimated results: explain if food expenditures are different between males and females.

we see that the coefficient of the dummy variable is -67.89 , also the p value is 0.85
as the p value is not less than 0.05 , hence the variable is not statistically signficant for the model and can be removed from the model equation
so food expenditures are not different between the males and females

Question 2) comment on the statistical significance of your findings

the r2 values is 0.93 , this means the model is able to explaim 93% variation in the value of Y due to independent variables xi, Di and Dixi

coefficient of Xi is signficant , as the p value is 0.00 , which is less than 0.05 and hence we reject the null hypothesis in favor of alternate hypothesis
for every unit change in the value of xi , the value of Yi changes by 0.06 units

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