6. Two researchers are investigating the effects of time spent studying on the examination marks earned...

 

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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 hours spent studying, H, hours on primary study, P, and hours spent 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 10.1, 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): M = 45.6 + 0.15P + 0.21R (0.03) R = 0.243 (1) %3D (2.8) (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 M = 45.6 +0.21H + -0.05P (0.14) R = 0.243 (2) (2.8) (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 Rin 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- ity. Explain whether this assertion is correct. Is the negative coefficient of P implausible? 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 hours spent studying, H, hours on primary study, P, and hours spent 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 10.1, 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): M = 45.6 + 0.15P + 0.21R (0.03) R = 0.243 (1) %3D (2.8) (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 M = 45.6 +0.21H + -0.05P (0.14) R = 0.243 (2) (2.8) (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 Rin 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- ity. Explain whether this assertion is correct. Is the negative coefficient of P implausible?

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Solution 6 Given that a Here The regression model of researcher A has better excplanatory poche... View the full answer