Question #65333

Imagine that we have survey data of people’s food expenditure and their basic income and demographic characteristics (e.g. age, education, etc.)
a. Write the linear regression that you would run to answer the question whether people who eat more nutritiously earn more.
b. Can the regression estimate tell us whether eating more nutritiously causes higher income ? Why or why not?
c. Do you predict the coefficient of your regression above to be positive or negative?
d. Do you predict the coefficients b and d to be positive or negative if you regress income or
nutrition on education?
Incomei=a + b(educationi) +e
Nutritioni=c +d(educationi) +m
e. How might the results from part (c) and (d) affect the interpretation of the regression you ran in (a)?

Expert's answer

a. The linear regression to answer the question whether people who eat more nutritiously earn more is:

Income i = a*x + b, where x - sustenance of food, a, b - coefficients.

b. The regression estimate can tell us whether eating more nutritiously causes higher income.

c. We predict the coefficient of our regression to be positive because there is a direct relationship between income and eating more nutritiously.

d. We predict the coefficients b and d to be positive if we regress income or nutrition on education, because there also would be a direct relationship.

Income i = a + b (education) + e

Nutrition i = c + d (education) + m

e. The results from part (c) and (d) will not change the interpretation of the regression we ran in (a).

Income i = a*x + b, where x - sustenance of food, a, b - coefficients.

b. The regression estimate can tell us whether eating more nutritiously causes higher income.

c. We predict the coefficient of our regression to be positive because there is a direct relationship between income and eating more nutritiously.

d. We predict the coefficients b and d to be positive if we regress income or nutrition on education, because there also would be a direct relationship.

Income i = a + b (education) + e

Nutrition i = c + d (education) + m

e. The results from part (c) and (d) will not change the interpretation of the regression we ran in (a).

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