AP Statistics 5.3 A Calculate a Predicted Response Value Using a Linear Regression Model Questions

Calculate a predicted response from a linear regression equation and identify whether the input is interpolation or less reliable extrapolation.

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

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 AP Statistics 5.3 A Calculate a Predicted Response Value Using a Linear Regression Model Questions 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 $\hat{y}=11.74+0.8247 x$ , and graph 2 shows the data with the line y=x.

GRAPH 1

GRAPH 2

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

Part (c):
The predicted arm span is $\hat{y}=11.74+0.8247 x=11.74+0.8247(61)=62.05$ inches.

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AP Statistics 5.3 A Calculate a Predicted Response Value Using a Linear Regression Model Questions question 1