6. Following are the scores on a teacher certification test administered prior to hiring (x) and the principal’s ratings of teacher effectiveness after three months on the job (y) for a group of six first-year teachers (A-F):
x 14 24 21 38 34 49
y 7 4 10 8 13 11
a. compute the summary statistics required for determining the regression equation for predicting principal ratings from teacher certification test scores.
b. using values from problem 6a, calculate the intercept and slope; state the regression equation.
c. suppose that three teachers apply for positions in the school, obtaining scores of 18, 32, 42, respectively, on the teacher certification test. Compute their predicted ratings of teacher effectiveness.
d. if in fact these data were real, what objections would you have to using the equation from Problem 6b for prediction in a real –life situation?
12. (No calculations are necessary for this problem). Suppose the following summary statistics are obtained from a large group of individuals:
_ _
X=52.0, Sx=8.7, Y=147.3, Sy=16.9. Dorothy receives an X score of 52. What is her predicted Y score if:
a. r = 0?
b. r = -.55?
c. r = +.38?
d. r = -1.00?
e. state the principle that emerges from your answers to problem 12a to 12d
f. show how formula (8.5) illustrates this principle.