Question

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%

Answer 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?

Answer: 77.94%

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%