Question

# A manager at a local bank analyzed the relationship between monthly salary (y, in \$) and...

A manager at a local bank analyzed the relationship between monthly salary (y, in \$) and length of service (x, measured in months) for 30 employees. She estimates the model:

Salary = β0 + β1Service + ε. The following ANOVA table summarizes a portion of the regression results.

 df SS MS F Regression 1 555,420 555,420 7.64 Residual 27 1,962,873 72,699 Total 28 2,518,293 Coefficients Standard Error t-stat p-value Intercept 784.92 322.25 2.44 0.02 Service 9.19 3.20 2.87 0.01

How much of the variation in Salary is unexplained by the sample regression equation?

77.94%

2%

18.39%

1%

A manager at a local bank analyzed the relationship between monthly salary (y, in \$) and length of service (x, measured in months) for 30 employees. She estimates the model:

Salary = β0 + β1Service + ε. The following ANOVA table summarizes a portion of the regression results.

 df SS MS F Regression 1 555,420 555,420 7.64 Residual 27 1,962,873 72,699 Total 28 2,518,293 Coefficients Standard Error t-stat p-value Intercept 784.92 322.25 2.44 0.02 Service 9.19 3.20 2.87 0.01

How much of the variation in Salary is unexplained by the sample regression equation?

2%

18.39%

1%

Coefficient of determination = R square = SSR/SST =555420/2518293 = 0.220554

Therefore Explained variation = 22.06%

Unexplained variation = 100%-22.06% = 77.94%

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