Question

(a) A company would like to predict how its trainees in sales will perform based on the results of aptitude test that is given to them at the beginning of the training. The table below contains the test scores (x values) and the values of the sales for these trainees during the first month of working at the company (y values in hundreds of dollars). Salesman 1 2 3 4 5 6 7 8 9 1.8 2.6 2.8 3.4 3.6 4.2 4.8 5.2 5.4 y 5.4 6.4 6.0 6.2 6.8 7.0 7.6 7.3 7.6 The summary statistics for these data are: Sum of the x data: 33.8 Sum of the squares of data 139.24: Sum of the y data: 60.3 Sum of the squares of y data: 408.61 Sum of the products of x and y data: 233.6 i. Draw a scatter diagram of these data on the graph paper provided. Label the diagram carefully. ii. Calculate the least squares line of y on r and draw the line on the scatter diagram iii. What level of sales would you expect from a salesman who scored 4.0 on the aptitude test? iv. Would you use the least squares line in part (ii.) to predict the sales of a salesman that scored 7.0 on the aptitude test? Justify your answer.

Answer 1

Scatter plot 9 8 y = 0.580x + 4.520 7 6 y Thousands of dollars 2 1 0 0 1 2 3 4 5 0 х

y = a + bx nx-X*Xy_9* 233.6–33.8*603 b= = 0.5803 9*139.24 - (33.8) y- bx 60.3-(0.5803B3.8 = 4.5207 9 line of regressio is y = 4.52 +0.58x a= x=4 y = 4.52 +0.58(4)=6.84 No the line in part a cannot be used as te point x = 7 does not lie in the range of x values. We cannot extrapolat e using line of regression