# 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?

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