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AP Statistics 5.3 Linear Regression Models Questions

Use a fitted linear model to calculate predicted responses and changes, while distinguishing interpolation from unreliable extrapolation.

Syllabus
Effective Fall 2026
Course
AP Statistics

Exam points

  • substitute a contextual explanatory value into y-hat equals intercept plus slope times x
  • use the regression slope and a change in x to calculate the corresponding change in predicted response
  • identify extrapolation beyond the observed x-range and explain why its prediction is less reliable

Covered syllabus points

5.3.A—Calculate a predicted response value using a linear regression model

Question 1

A student measured the heights and the arm spans, rounded to the nearest inch, of each person in a random sample of 12 seniors at a high school. A scatterplot of arm span versus height for the 12 seniors is shown.

Figure for Question 1 — AP Statistics

Let x represent height, in inches, and let y represent arm span, in inches. Two scatterplots of the same data are shown below. Graph 1 shows the data with the least squares regression line y^=11.74+0.8247x\hat{y}=11.74+0.8247 x, and graph 2 shows the data with the line y=x.

GRAPH 1

GRAPH 1

GRAPH 2

GRAPH 2

Using the best model for prediction, calculate the predicted arm span for a senior with height 61 inches.

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