Consider the following dummy variable regression function where food expenditure

Question

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.

estimate the regression function to examine whether food expenditure is different across genders.

Yi = 1432.57 + .06xi - 67.89Di- .006Dixi

A=1432.577

Xi (Income)=.0615

DI (Dummy Variable)= -67.89

DX = -.006

Prob. (.00) (.00) (.85) (.64)

R^2=.93

R^2adj = .90

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

Question 2) comment on the statistical significance of your findings

Question 3) To allow interactions between X and D estimate the following regression function

Explanation / 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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