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9.3 Justifying a Claim About the Slope of a Regression Model Based on a Confidence Interval

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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Using the Slope CI to Make Claims

The confidence interval for β{\beta} gives a range of plausible values for the true slope.

Key question: Is there convincing evidence of a linear relationship?

  • If CI contains 0: β=0{\beta = 0} is plausible → no convincing evidence of a linear relationship
  • If CI is entirely positive: Evidence that β>0{\beta > 0} (positive linear relationship)
  • If CI is entirely negative: Evidence that β<0{\beta < 0} (negative linear relationship)

Example: 95% CI for β{\beta} = (0.29,0.87){(0.29, 0.87)}

Since the entire interval is positive and does not include 0, we have convincing evidence of a positive linear relationship between x{x} and y{y}. For each one-unit increase in x{x}, the true mean y{y} increases by between 0.29 and 0.87 units.

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 IntervalThis 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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