STAT 440 - Forecasting
Lecture Review #8 - Regression Review

It’s time once again to investigate the importance of sleep upon "knowledge festival" performance … and (incidentally) to review regression calculations. The data below are from six of Dr. Rasp’s imaginary friends.

Work together with your partner(s) to answer the following questions. DO THE COMPUTATIONS … don’t just rely on Excel’s black box. (Why not?) You can work things either on this sheet or in your class notes.

a) ALWAYS DRAW A PICTURE!!! Does a linear model appear reasonable for these data?

b) What is the (sample) variance of the "sleep" data? Of the "grade" data?

c) What is the covariance between sleep and grade, for these data? What does this number mean?

d) What is the slope of the regression line, for these data? How is it found? Why are we finding it that way? What does it mean?

e) What is the intercept of the regression line, for these data? How is it found? Why are we finding it that way? What does it mean?

f) What is the correlation between sleep and grade, for these data? What does it mean? Find a (very non-traditional) 42% confidence interval for the true population correlation.

g) For each person in the data set, find the grade that he/she/they would be expected to get, given the amount of sleep he/she/they got.

h) For each person in the data set, find the prediction error. That is, how much better/worse than expected did he/she/they do? What do these errors add to? Why?

i) Give the error variance for the model. Interpret this number.

j) What is the predicted average grade for students who get 4 hours of sleep? Give a 95% confidence interval for this quantity.

k) Gregorivich, another of Dr. Rasp’s imaginary friends, got 4 hours of sleep before the k.f. What is his predicted grade?

l) Which of your two previous answers (to parts j and k) will be more accurate? Why? (Or will they have the same accuracy?)

m) Herkimer, yet another of Dr. Rasp’s imaginary friends, got 6 hours of sleep before the k.f. What is his predicted grade?

n) Will your prediction for Gregorivich or for Herkimer be more accurate? Why?