What should R2 be if all independent variables are able to fully explain y by our model?
statistics
Description
Revision
CALCULATION
QUESTIONS
The following outputs were generated when Excel was used:
|
SUMMARY
OUTPUT |
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|
Regression Statistics |
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|
Multiple R |
0.9019 |
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|
R Square |
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|
Adjusted R
Square |
0.7668 |
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|
Standard
Error |
328.4111 |
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|
Observations |
*1 |
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|
ANOVA |
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|
|
df |
SS |
MS |
F |
Significance F |
|
|
Regression |
*2 |
*4 |
1881222.0224 |
*7 |
0.0001 |
|
|
Residual |
*3 |
*5 |
*6 |
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|
Total |
15 |
6937912.0000 |
|
|
|
|
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
Intercept |
-64.5812 |
985.2699 |
-0.0655 |
0.9488 |
-2211.2999 |
2082.1376 |
|
X Variable 1 |
27.4377 |
*8 |
4.0747 |
0.0015 |
810.0000 |
42.1093 |
|
X Variable 2 |
1.3093 |
1.8227 |
*9 |
0.4863 |
*10 |
*11 |
|
X Variable 3 |
1.1780 |
0.7831 |
1.5042 |
0.1584 |
*12 |
2.8842 |
a.
Complete the
empty fields (with * - there are 12 of it) in the above table.
b.
Find R2.
Explain what the number tells you about this regression model.
c.
What should R2
be if all independent variables are able to fully explain y by our model?
d.
Test whether y
is related to any of the X’s (the overall significance of the model). Use a significance level of 0.01.
- Find the
value of y if :
X1:73
X2: 300
X3: 250
Question
a.
What is the
standard error of the multiple regression model when k=4
n=100 SSExplained=200, SSTotal=1720
b. Explain briefly 3 assumptions of CLRM?
c.
Find the
value of A in the following :
(i)
P ( Z > 100
) = A
(ii)
P( t > B )
= 0 .98 assuming n=10
(iii)
P(t > 2.831)
= C assuming n=21
d. Given
E(X) = 7, E(Y) = 12, E(XY) = 48, Var(X) = 16,
Var(Y) =25, and X and Y are
independent events, compute:
E(4X
- 6Y)
Cov(5X,3Y)
Cov( X+2Y, 4X-2Y)
