Question

Problem 8 (20 marks) The general manager of a chain of department stores believes that experience is the most important factor in determining the level of success of a salesperson. To examine this belief, she records last month's sales (in $1,000s) and the years of experience of 10 randomly selected salespeople. These data are listed below. Salesperson 1 2 3 4 5 6 7 8 9 10 Years of Experience 3 2 10 3 8 5 12 7 20 15 Sales 7 9 20 15 18 14 20 17 30 25 Assume normality of variables. a) Calculate the coefficient of correlation r. Provide an interpretation of the computed value of r. (9 marks) b) Calculate the coefficient de determination r square (R2). Provide an interpretation of the computed value of r square (R2). (3 marks) c) Determine the least squares line. Provide an interpretation of your results. (8 marks)

Answer 1

et X C yearsof experience) 3 2 10 3 8 15 12 7 205 Y (sales) 7 9 20 1518 14 20 17 302 0.) Coefficient of correlation () = Elai-7) Wi-J) Exi-2) 2 E14 -92 0.9528 9t means 6 that there is very po strong direct relationship between X and y. coefficient of determination R² = (0.9528)² = 0.90 79 that go.8% of the variability of y is explained by X 96 means с) 9 Bot B ý ß BE Ili-2) 19-9) Tri-)? Y = 7.9 462 + 1.12402 1.12 40 Slope of line is the sales per unit change in experience f. 1240. increase Interapt teron is 7.9462,