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# Simple Linear Regression and Correlation (3).docx

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McMaster University

Statistics

STATS 2B03

Aaron Childs

Fall

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November 13 , 2012
Stats 2B03: Statistical Methods for Science
Simple Linear Regression and Correlation (3)
9.4.2 t-test for 0 : 1 =0, A : 1 ≠0
- y = β0+ β 1
- H 0 no linear relationship between y and x
- H A there is a linear relationship
- Notes:
If H0is not rejected then the regression line ŷ = β0hat+ β1hat should
not be used
If H0is not rejected there could be some other relationship between y
2
and x, for example y = β 0 β 1 + β 2
If H0is not rejected, we can not conclude that there is no linear
relationship between y and x. we can only conclude that there is not
strong evidence of a linear relationship based on the given data
- procedure:
step 1: calculate
, where √
√
step 2: reject H0if |n-2>tn-2, 1-α
- example (continued):
√
√
do not reject H 0ince 2.6988<4.3027
9.4.3 ANOVA for Regression
- The hypothesis H : 0 =1, H : A ≠1 can also be tested using the following
procedure:
Step 1: calculate
Step 2: reject H if F

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