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9.2 Confidence Intervals 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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Confidence Interval for the Slope Beta

Parameter: β{\beta} = the true slope of the population regression model relating y{y} to x{x}

Conditions (LINE):

  • Linear: Scatterplot shows linear trend; residual plot has no curved pattern
  • Independent: Observations are independent (10% condition for random samples)
  • Normal: Residuals are approximately normal — check with histogram or Normal probability plot of residuals
  • Equal variance: Residual plot shows consistent vertical spread across all x{x} values
Formula:
b±t∗⋅SEbdf=n−2b \pm t^* \cdot SE_b \quad df = n - 2

where t∗{t^*} is from the t-distribution with n−2{n-2} degrees of freedom.

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 ModelThis 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 ModelPreview lesson
  5. 9.5Carrying Out a Test for the Slope of a Regression ModelPreview lesson

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