Question

7. The following table list s manager ratings of job performance and attitude for several employees: Performance (x)--59-63-65-69-m-76_.69-SA Attitude (y) 72 67 78 82 87 92 83 78 a) Plot the scatter diagram for the paired data b) Assuming a 5% level of significance, use hypothesis testing and the linear correlation coefficient (r) to determine if there is a linear correlation. c) Find the equation of the regression line and plot it on your scatter diagram using an x of 60 and an x of 74. Determine the residual value for an x of 76 and explain its meaning Determine the coefficient of determination. d) e)

Answer 1

b)

1 Y Predict Erro Error 2 2 59 3 63 65 72 67 78 82 3481 3969 4225 4761 5929 5776 4761 40966084 248 69.9505 2.0495 4.2007 4221 74.4874 7.4874 56.0610 5070 76.7559 1.2441 1.5479 5658 81.2928 0.7072 0.5001 6699 90.36673.3667 11.3344 6992 89.2324 2.7676 7.6594 5727 81.2928 1.7072 2.9146 4992 75.6216 2.3784 5.6567 639 -4.3E-14 89.8748 6724 7569 84646 mean of the data 92 83 78 639 7 76 = mean of the y data =- 10 542 3699851487 43607 67.75 79.875 7621.6 10654.9 8973.2 Scatter Plot y bar y 1.1342x + 3.0306 R1 0.7989 slope b = intercept a= 1.134 3.031 16 Correlation r 0.894 18 Scatter Plot R Sqaure 0.7989 Linear (Scatter Plot) 24

The following needs to be tested: where ρ corresponds to the population correlation. The sample size is n 8, so then the number of degrees of freedom is df-n-2-8-2-6 The corresponding critical correlation value rc for a significance level of a 0.05, for a two-tailed test is: e 0.707 Observe that in this case, the null hypothesis Ho : ρ = 0 is rejected if Irl > re = 0.707. Based on the sample correlation provided, we havethat0.894>Te concluded that the null hypothesis is rejected. 0.707, from which is

c)

y = 1.13422.+ 3.0306

y = 1.1342 * 60 3.0306 = 71.0826

y = 1.1342 * 74 3.0306 = 86.9614

d)

Residual = Actual - Predicted =

2.7676

positive residual means they are above the regression line

e)

Coefficient of determination = R square = 0.894*0.894 = 0.7989