Question

6. Two researchers are investigating the effects of time spent studying on the examination marks earned by students on a certain course. For a sample of 100 students, they have the examination mark, M, total ours spent studying, H, on revision. R. By definition, H = P+ R. The sample means of H. P. and R are 100 hours, 95 hours, and 5 hours, respectively. The sample correlation coefficients are 0.98 for H and P, and 0.10 for H and R, and -0.11 for P and R. The standard deviations of the distributions of H, P, and R are 10., 10.1 and 2.1, respectively Researchers A decides to regress M on P and R and fit the following regression(standard errors in parentheses) hours on primary study, P, and hours spent M 45.60.15P 0.21R R2 0.243 (1) (2.8) (0.03 (0.14) Researchers B decides to regress M on H, P and R. However, the regression application refuses to fit the regression with all three ex planatory variables. Instead, it drops R and the regression output is R2-0.243 M-45.6 +0.2 1H +-0.05P (2) (2.8) (0.14) (0.14) (a) Researcher A says that her specification has better explanatory power than that of Researcher B because the coefficient of her main variable, P, has a high t statistic. Explain whether this assertion is correct (b) She says that the insignificant coefficient of R in 1) is to be expected because the students, on average, spent much less time on revision than on primary study. Explain whether this assertion is correct (c) Researcher B says that, assuming that his specification is in fact correct, not being able to include R in the regression has given rise to omitted variable bias, and this is responsible for the negative coefficient of P. Explain whether this assertion is correct. (d) A commentator, drawing attention to the high correlation be- tween H and P, says that the real reason for the implausible neg- ative coefficient of P obtained by Researcher B is multicollinear- itv. Explain whether this assertion is correct. coefficient of P implausible? Is the negative

Answer 1

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