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):
(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 this school, obtaining scores of 18, 32, and 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?