Question

Joe from Joe’s Test Prep and Coffee shop wants to demonstrate that receiving formal tutoring increases performance on the SAT test. In order to do so, he calls on an independent researcher to evaluate the final SAT scores for a large random sample of high school seniors. The researcher produces the following table to summarize her Ordinary Least Squares Regression analysis.

Table 1. Ordinary Least Squares Regression analysis of SAT scores among a sample of high school seniors.. Model 2 Model 1 Hours of tutoring 1.9** 0.7 Family income ($1000s) 16.3 Constant 490.0 427.2 Model R-squared 0.321 0.480 p<.05; "p<.01;p.001 n 425

2: Consider the researcher’s decision to include family income as a predictor in Model 2.

• What do you think might have been her motivation for including income as a control in investigating the effect of tutoring on SAT performance?
• Draw a casual diagram to summarize the potential role of income in the relationship between tutoring and SAT performance.
• Do the results of Model 2 support Joe’s claim that formal tutoring has a causal intact on SAT performance? Explain your answer.

Answer 1

(1a) n=25

(1b)In model 1,  the coefficient of hours of tutoring  =1.9 ,it has positive sign so there is increasing effect of hours of tutoring on the response variable SAT scores. It has double star (**) , it means it is significant at alpha=0.01.

if we increase one unit of hours of tutoring the SAT scores will increase by 1.9 unit

(1c) if the hours of tutoring is zero than there will be intercept=490 SAT scores

(1d) here the model is SAT_Score=490+1.9*Hours_of_Tutoring

for Hours of Tutoring=20, then SAT Scores=590+1.9*20=628

(1e) coefficient of determination=Model R-squared=0.321

(1f) in model 2, the coefficient of hours of tutoring  =0.7 ,it has positive sign so there is increasing effect of hours of tutoring on the response variable SAT scores. It has not any star , it means it is not significant at alpha=0.05

.in model 2, the coefficient of family income =16.3 ,it has positive sign so there is increasing effect of family income on the response variable SAT scores. It has two star , it means it is significant at alpha=0.01

(1g) if the hours of tutoring and family income are zero than there will be intercept=427.7 SAT scores

(1h) here the model is SAT_Score=490+0.7*Hours_of_Tutoring+16.3*family_income

for Hours of Tutoring=20, and family income=50 thousand  then SAT Scores=490+0.7*20+16.3*50=1319

(1i)coefficient of determination=Model R-squared=0.480

(2) yes, inclusion of variable family  income is motivating as it has significant impact and cosiderable increase in R-squared.

also the tutoring effect is casual as in the model2, it is not significant.