Question: A sample of 30 students are randomly selected from a large chemistry class. Using data from this sample, a multiple linear regression equation is calculated to predict the score of a student on the final

exam (F) based on the number of hours spent studying for the exam (S), the score on the midterm exam (M), and the number of classes missed during the quarter (C) . The sample regression equation is:

F = 57 + 4S + 0.1M – 2C.

a) With all other things being equal, as the number of missed classes increases, the predicted final exam score: ( increases or decreases)?

a) Find the predicted final exam score for a student who studied for 4 hours, scored 78 points on the midterm exam, and missed 5 classes during the quarter.

b) Find the residual for a student who has the above values for the explanatory variables and scores a 68 on the final exam.

c) The Standard error for the missed classes coefficient (C) is 0.5, Give a test statistic for testing whether the true regression coefficient for the missed classes variable is different from zero.

d) Based on the test statistic in part d) , can we conclude the regression coefficient for the missed classes variable (C) is significantly different from zero? Explain.