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9.1 Introducing Statistics: Do Those Points Align?

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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The Population Regression Model

In Unit 2, we studied the sample regression line y^=a+bx{\hat{y} = a + bx} as a description of a dataset. Now we consider the population model:

y=α+βx+εy = \alpha + \beta x + \varepsilon

where:

  • α{\alpha} = population y-intercept (true intercept)
  • β{\beta} = population slope (the parameter of interest)
  • ε{\varepsilon} = error term (random variation around the true line)

Conditions for regression inference (LINE):

  • Linear: The true relationship between x{x} and y{y} is linear
  • Independent: Observations are independent
  • Normal: For each value of x{x}, the y{y} values are normally distributed around the true line
  • Equal variance: The standard deviation of y{y} is the same for all x{x} (homoscedasticity)

The sample slope b{b} is an estimate of the population slope β{\beta}.

In this unit

5 lessons

  1. 9.1Introducing Statistics: Do Those Points Align?This 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 ModelPreview lesson
  5. 9.5Carrying Out a Test for the Slope of a Regression ModelPreview lesson

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