Hypothesis tests in linear regression

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Presentation transcript:

Hypothesis tests in linear regression Slope: H0: 1 = 1,0 H1: 1  1,0 Reject H0: 1 = 1,0 if |t0|>t/2,n-2 Intercept: H0: 0 = 0,0 H1: 0  0,0

Hypothesis tests in linear regression Special case: H0: 1 = 0 H1: 1  0 Fail to reject H0: 1 = 0 is equivalent to concluding that there is no linear relationship between x and Y.

Example: Sales vs. Advertising

Analysis of variance Test for significance of regression. Analysis of variance identity Symbolical equation

Analysis of variance Test statistics Reject H0: 1 = 0, if f0>f,1,n-2

Confidence intervals Confidence interval on the slope Confidence interval on the intercept

Confidence interval on the mean response