Question
In: Statistics and Probability
Complete the following answers to the ANOVA summary table for a simple linear regression. SSError=120, SST=480,...
Complete the following answers to the ANOVA summary table for a simple linear regression. SSError=120, SST=480, and dfT=7.
|
Source |
SS |
df |
MS |
F |
|
Regression |
|
|
||
|
Error |
120 |
|||
|
Total |
480 |
7 |
SSRegression=?
dfRegression=?
dfError=?
MSRegression=?
MSError=?
F=?
What proportion of variation is accounted for by the simple linear regression?
Solutions
Expert Solution
Solution:
Given:
SSError=120, SST=480, and dfT=7.
We have to complete ANOVA table:
SSRegression=...........?
SSRegression= SST - SSError
SSRegression= 480 - 120
SSRegression= 360
dfRegression= ........?
Since this is simple linear regression problem, thus k = number of independent variables = 1
thus
dfRegression= k
dfRegression= 1
thus
dfError= dfT - dfRegression
dfError= 7 - 1
dfError= 6
MSRegression=...........?
MSRegression= SSRegression / dfRegression
MSRegression= 360 / 1
MSRegression= 360
MSError=............?
MSError= SSError / dfError
MSError= 120 / 6
MSError= 20
F= MSRegression / MSError
F = 360 / 20
F = 18
Thus
| Source | SS | df | MS | F |
|---|---|---|---|---|
| Regression | 360 | 1 | 360 | 18 |
| Error | 120 | 6 | 20 | |
| Total | 480 | 7 |
What proportion of variation is accounted for by the simple linear regression?
That is find Coefficient of determination, that is R2
Thus 75% of variation is accounted for by the simple linear regression
orchestra answered 2 years agoRelated Solutions
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