Suppose the MU decides to model students’ GPA as a linear function of
time spent in lectures (T) in hours, such that GPAi = α + βTi + µi. Where,
µ is a disturbance term.
The results of the estimated model were as follows, but some of them were
lost due to the problem of electricity in the computer room,hence need to be
calculatedusing your simple calculator.
GPA = 0.5681 + 0.01022T.
Std error (0.928) (…….) R-square = 0.58.
t-statistic (……) (2.863) N = 55.
Required:
a)Fill in the missing values.
b)Interpret the results.
c)Test the hypothesis that β1 = 0. Can we conclude that attending lectures
significantly improve student GPA?
a) The missing values are the standard error and the t-statistic. The standard error is 0.928 and the t-statistic is 2.863.
b) The results indicate that there is a positive relationship between time spent in lectures and GPA, with a coefficient of 0.01022. This means that for every additional hour spent in lectures, the student's GPA increases by 0.01022. The R-squared value of 0.58 indicates that 58% of the variation in GPA can be explained by the variation in time spent in lectures.
c) To test the hypothesis that β1 = 0, we can use the t-statistic. The t-statistic is 2.863, which is greater than the critical value of 1.96. This indicates that the null hypothesis can be rejected, and that attending lectures does significantly improve student GPA.