Question

1 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 Years of Experience Sales 3 7 2 2 9 3 10 4 3 15 5 8 18 6 5 14 7 12 20 8 7 17 9 30 10 15 25 20 20 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

1.Correlation coefficient r:

Use "=CORREL(Array 1, Array 2)" Formual to calculate the r value in excel.

r = 0.95. It is a prefect straight line positive linear correlation between the variables

Clipboard Font Alignment E4 fx =CORREL(A2:A11,B2:B11) с D E F C لا لا لا Nw re 0.95 A B 1 Years of Experience Sales 2 3 3 2 4 10 5 3 6 8 7 5 8 12 9 7 10 20 11 15 12 7 9 20 15 18 14 00 20 17 30 25 13 14 16

Coefficient of determination :

Select both years of experience and sales and insert the scatter plot.

- Right click any one of the data point and add trend line.

- In the format trendline option select "Linear" and also select "Display an equation on chart" and "Display R-squared value"

Coefficient of determination = 0.908

с z D E F G J H - K L M o Format Trendline Trendline Options 35 + 7 9 20 15 18 14 30 y = 1.124x + 7.946 R2 = 0.908 O Linear 25 Y 20 17 30 25 bit Logarithmic 20 O, 15 O O Polynomial Order بن Power 10 A B 1 Years of Experience Sales 2 3 3 2 4 10 5 3 6 8 7 5 8 12 9 7 10 20 11 15 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Sheet1 Moving Average Period 2 5 Trendline Name 0 0 5 10 15 20 25 Linear (Sales) O Automatic Custom Forecast Forward 0.0 periods Backward 0.0 periods Set Intercept 0.0 ✓ Display Equation on chart ✓ Display R-squared value on chart

Least square regression equation:

y = 1.124x + 7.946

35 30 y = 1.124x +7.946 R? = 0.908 25 20 15 10 5 0 0 5 10 15 20 25