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# Multiple Regression and Correlation (2).docx

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McMaster University

Statistics

STATS 2B03

Aaron Childs

Fall

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November 21 , 2012
Stats 2B03: Statistical Methods for Science
Multiple Regression and Correlation (2)
10.3 The Multiple Regression Equation
- example: from the Databank data set
y = blood pressure
x1= weight
x = age
2
then from Minitab output #25 on page 74 of the courseware is for the
model y = β 0 β x1 1β x 2 2rom the output we see that ŷ = 87.899 +
.15292x +1.50530x , e2g. if someone is 38 years of age and weighs
200lbs, then their blood pressure is predicted to be ŷ = 87.899 +
.15292(200) + .50530(38) = 137.68
10.4.1 Evaluating the multiple regression equation: overall F-test
- the ANOVA table for multiple regression is as follows,
Source SS d.f. MS F
Regression SSR K SSR/k MSR/MSE
Error SSE ∑ n-k-1 SSE/n-k-1
Total SST (syy n-1
- k = # of x-variables
- the F-statistic in this ANOVA table tests the hypothesis H :0β =1β =2…= β = 0k
H : at least on β≠0
A i
- H0: no linear relation between y and may of the x-variables
- HA: a linear relationship exist between y and at least one of the x-variables
- Example (continued):
From the Minitab output, the p-value (given under P in the ANOVA
table) for the above F-test is .000

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