4. An instructor asked five students how many hours they had studied for an exam.

The number of hours studied and their grades, along with the means, are shown here.

(a) Determine the linear prediction rule for predicting test grade from hours studied, and

(b) draw the regression line. Use the linear prediction rule to figure the predicted test grade of students who studied for each of the following number of hours:

(c) 3,

(d) 5, and

(e) 7.

(f) Determine the standardized regression coefficient, and (g) explain what you have done in all the previous parts of this question to someone who understands the mean and deviation scores but does not know any more about statistics. (h) Add the dots for the pairs of scores for the five students to your figure from part

(b) and also add a regression line for the linear prediction rule Yn

= 60 + 15.0021X2. (i) Which regression line does a better job of coming close to the dots in your figure for part (h), and why? (j) Figure the sum of squared errors for your linear prediction rule from part

(a) and for the prediction rule Yn

= 60 + 15.0021X2. (k) ADVANCED TOPIC: Find the proportionate reduction in error (using SS Error and SS Total).

Hours Studied Test Grade 0 52 10 95 6 83 8 71 6 64 M 6 73