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9.4 Setting Up a Test for the Slope of a Regression Model

Part of Inference for Quantitative Data: Slopes in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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Hypotheses for the Slope t-Test

Parameter: β{\beta} = the true slope of the population regression model

Hypotheses (most common):
H0:β=0(no linear relationship)H_0: \beta = 0 \quad \text{(no linear relationship)}
Ha:β≠0(there is a linear relationship)H_a: \beta \neq 0 \quad \text{(there is a linear relationship)}

Alternatively:

  • Ha:β>0{H_a: \beta > 0} (positive linear relationship)
  • Ha:β<0{H_a: \beta < 0} (negative linear relationship)

Conditions (LINE — same as for CI):

  • L: Linear relationship
  • I: Independent observations
  • N: Normal residuals
  • E: Equal variance
Test statistic:
t=b−0SEb=bSEbdf=n−2t = \frac{b - 0}{SE_b} = \frac{b}{SE_b} \quad df = n - 2

This t-statistic appears directly in computer output!

In this unit

5 lessons

  1. 9.1Introducing Statistics: Do Those Points Align?Preview lesson
  2. 9.2Confidence Intervals for the Slope of a Regression ModelPreview lesson
  3. 9.3Justifying a Claim About the Slope of a Regression Model Based on a Confidence IntervalPreview lesson
  4. 9.4Setting Up a Test for the Slope of a Regression ModelThis lesson
  5. 9.5Carrying Out a Test for the Slope of a Regression ModelPreview lesson

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