# Determine The Regression Equation Statistics Homework Help

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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?