Ans :
Given regression equation
= 0.86 + 0.65 x1
Ingeneral regression equation line
= + *
From the given regression equation
= 0.86
= 0.65
a) Coefficients
Term | Coef | SE Coef | T value | p value | VIF |
Constant | 0.86 | 1.38 | 16.58 | 0.000 | |
x1 | 0.65 | 0.231 | 7 | 0.000 |
Ans b) :
One way ANOVA
Source |
DF |
SS |
MS |
F |
regression |
k |
SSregression |
SSTreatment /k |
MSTreatment/MSError |
Error |
n-k-1 |
SSError |
SSError /n-k-1 |
|
Total |
in-1 |
SSTotal |
Now to calculate missing values
1)we know that MSreg = SSreg/dfreg
degrees of freedom of regression =SSreg/ MSreg = 2.12/2.12 =1
2)degrees of freedom of error = df total -df of regression =9-1 = 8
3)SSE = SST -SSregression = 3.10-2.12 =
Source |
DF |
SS |
MS |
F |
regression |
1 |
2.12 |
2.12 |
17.37 |
Error |
8 |
0.98 |
0.12 |
|
Total |
9 |
3.10 |
c) Ans :
Given regression equation :
= 0.35+0.26X1 + 0.13X2 +0.46X3
Term | Coef | SE Coef | T |
Constant | 0.35 | 0.53 | 0.65 |
X1 | 0.26 | 0.09 | 2.89 |
X2 | 0.1 | 0.138 | 0.943 |
X3 | 0.46 | 0.12 | 3.83 |
d) ans :
ANOVA Table
Source |
DF |
SS |
MS |
F |
regression |
k |
SSregression |
SSTreatment /k |
MSTreatment/MSError |
Error |
n-k-1 |
SSError |
SSError /n-k-1 |
|
Total |
in-1 |
SSTotal |
Calculate missing values in given ANOVA table
1)SSE = SST -SSregression 3.11 - 2.75 = 0.36
2) we know that MSError =SSError/df
df error = SSError / MSError = 0.36/0.06 = 6
3)df regression = k = 3
4) df total = df regression +df error = 6+3 = 9
5) MSTreatment = 2.75/3 = 0.9166
6) F = 0.9166/0.06 = 15.2766
ANOVA Table
Source |
DF |
SS |
MS |
F |
regression |
3 |
2.75 |
0.9166 |
15.2766 |
Error |
6 |
0.36 |
0.06 |
|
Total |
9 |
3.11 |
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