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Confirm in testing the single restriction b1=0 that the t test is equal to the F...

Confirm in testing the single restriction b1=0 that the t test is equal to the F test.

Expert Solution

The procedure of testing for a linear association between the response and predictor variables using the analysis of variance involves using the F–distribution. This is the same distribution we used in the 1-Way ANOVA. The testing procedure is as follows:

1. H0 : β1 =0 HA:β1=0 (This will always be a 2–sided test)

2.Test Statistic: Fobs = MSR /MSE

3. Rejection Region.: Fobs >F1,n−2,α

4. p-value: P(F>Fobs)

Note that we already have a procedure for testing this hypothesis, (The procedure to test if β1 is equal to some value, say β01. • H0 :β1 =β01 (β01 specified, usually 0)

• (1) Ha : β1= β01

(2) Ha : β1 >β01

(3) Ha : β1 <β01

• Test Statistic:tobs = b1−β01/( se/ √SSxx) = (b1−β01)/sb1

• Rejection Region

(1) RR: |tobs|≥tα/2,n−2

(2) RR : tobs ≥ tα,n−2

(3) RR : tobs ≤−tα,n−2

• (1) P–value: 2 ·P(t ≥|tobs|)

(2) P–value: P(t ≥ tobs)

(3) P–value: P(t ≤ tobs))

but F-test is an important lead–in to multiple regression.

orchestra answered 1 year ago

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