TESTING THE STRENGTH OF THE MULTIPLE REGRESSION MODEL. Test 1: Are Any of the x’s Useful in Predicting y?. We are asking: Can we conclude at least one of the ’s (other than 0 ) 0? H 0 : 1 = 2 = 3 = 4 = 0 H A : At least one of these ’s 0 = .05.
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MULTIPLE REGRESSION MODEL
We are asking: Can we conclude at least one of the ’s (other than 0) 0?
H0: 1 = 2 = 3 = 4 = 0
HA: At least one of these ’s 0
MSR = SSR/DFR
MSE = SSE/DFE
F = MSR/MSE > F,DFR,DFE
DFE = Total DF- DFR
Total DF = n-1
Total SS = (yi - )2
MSE = SSE/DFE
F = MSR/MSE
P-value for the F test
H0: 3 = 0 (x3 is not significant in this model)
HA: 3 0 (x3 is significant in this model)
t-value for test of 3 = 0
p-value for test of 3 = 0
p-value for land is .00000717. Predicting y?
In this model Land is significant.
EXAMPLES IN WHICH THIS MIGHT HAPPEN:
This is discussed in a future module.
R2 might be higher – but adjusted R2 might be much lower
Scatterplot Due to Changes in the x’s?
This is not what is really going on
4 Places to Look on Excel Printout Due to Changes in the x’s?
What proportion of y can be
explained by changes in x?
2- Significance F
Are any variables useful?
3- p-values for t-tests
Which variables are significant
in this model?