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 = β_{0} + β_{1}Service + 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  tstat  pvalue  
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 = β_{0} + β_{1}Service + 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 
tstat 
pvalue 

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%
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