Suppose you have a sample of 20 high school students providing data for the score on the math portion of the SAT and family (household) income for each individual student. You hypothesize the following theoretical relationship: SATmathi = β0 + β1FamilyIncomei + εi The estimated relationship you obtain using this data is: I i Family Income is measured in thousands ($1000) of dollars per year SATmath is the score on the math portion of the SAT, out of 800 points 

a. Give a one-sentence interpretation of the slope coefficient of this model. 

b. What is the predicted (or estimated) SAT math score for a student whose family earns $50,000 a year? 

c. How much higher would we expect the score of a student whose family income is $100,000 to be than that of a student whose family income is $40,000? 

d. What would happen to the estimated coefficient on family income if we had measured it in dollars, rather than in thousands of dollars? 

e. What factors besides family income are likely to influence a student’s SAT math score? (I.e., what would the error term be capturing in this model?) 

f. Use the data below to calculate the predicted score and the residual for each observation in your sample using this estimated model (no need to do all 20 by hand, you can use Excel as a shortcut – and if you do calculate by hand, only calculating five observations by hand as practice will be sufficient for this part of the problem):