Job proficiency. a personnel officer in a governmental agency administered four newly developed aptitude tests to each of 25 applicants for entry-level clerical positions in the agency. for purpose of the study, all 25 applicants were accepted for positions irrespective of their test scores. after a probationary period, each applicant was rated for proficiency on the job. the scores on the four tests (x_1, x_2, x_3, x_4) and the job proficiency score (y) for the 25 employees were as follows: a. prepare separate stem-and-leaf plots of the test scores for each of the four newly developed aptitude tests. are there any noteworthy features in these plots? comment. b. obtain the scatter plot matrix. also obtain the correlation matrix of the x variables. what do the scatter plots suggest about the nature of the functional relationship between the response variable y and each of the predictor variables? are any serious multicollinearity problems evident? explain. c. fit the multiple regression function containing all four predictor variables as first-order terms. does it appear that all predictor variables should be retained?