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A consultant is interested in seeing how accurately a new job performance index measures what is important for a corporation. The consultant is interested in the relationship between the annual employee salary or SALARY (Y in $1,000s) and the job performance index or JPI (X). A random sample of 14 employees is selected, yielding the following.
|
JPI |
SALARY |
PREDICT |
|
9 |
66 |
6 |
|
7 |
55 |
10 |
|
8 |
63 |
|
|
4 |
45 |
|
|
7 |
58 |
|
|
5 |
49 |
|
|
5 |
50 |
|
|
6 |
52 |
|
|
4 |
46 |
|
|
7 |
56 |
|
|
7 |
60 |
|
|
7 |
54 |
|
|
8 |
60 |
|
|
6 |
52 |
Correlations: JPI, SALARY
Pearson correlation of JPI and SALARY = 0.966
P-Value = 0.000
Regression Analysis: SALARY versus JPI
The regression equation is
SALARY = 29.0 + 4.00 JPI
Predictor Coef SE Coef T P
Constant 29.000 2.045 14.18 0.000
JPI 4.0000 0.3103 12.89 0.000
S = 1.68325 R-Sq = 93.3% R-Sq(adj) = 92.7%
Analysis of Variance
Source DF SS MS F P
Regression 1 470.86 470.86 166.18 0.000
Residual Error 12 34.00 2.83
Total 13 504.86
Predicted Values for New Observations
New Obs Fit SE Fit 95% CI 95% PI
1 53.000 0.469 (51.978, 54.022) (49.193, 56.807)
2 69.000 1.196 (66.394, 71.606) (64.501, 73.499)X
X denotes a point that is an extreme outlier in the predictors.
Values of Predictors for New Observations
New Obs JPI
1 6.0
2 10.0
a. Analyze the above output to determine the regression equation.
b. Find and interpret 
in the context of this problem.
c. Find and interpret the coefficient of determination (r-squared).
d. Find and interpret coefficient of correlation.
e. Does the data provide significant evidence (a = .05) that JPI can be used to predict Salary? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret.
f. Find the 95% confidence interval for mean salary when the JPI is 6. Interpret this interval.
g. Find the 95% prediction interval for the salary of an individual whose JPI is 6. Interpret this interval.
h. What can we say about the salary for a person with a JPI of 10?
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