Which set best describes the possible values of r-squared?

Answer: 0 to 1 (or 0% to 100%) r-squared is a proportion between 0 and 1 (commonly written as a percent 0%-100%).

What is the y-intercept?

Answer: 25 The line passes through (x-bar, y-bar): a = y-bar - b x-bar = 100 - 1.5(50) = 25.

Which statement is best supported?

Answer: Model B explains more of the variability in y Higher r-squared indicates a greater proportion of variability in y explained by the linear model.

AP Statistics · Topic 2.8

Least Squares Regression Practice

Part of Exploring Two-Variable Data.(DAT-1.E)

Practice questions

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Sample questions

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Sample 1difficulty 1/5
$Consider r-squared from a least-squares regression.$
$Which set best describes the possible values of r-squared?$
- A
  $0 to 1 (or 0% to 100%)$
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- B
  $any real number$
- C
  $0 to 100$
- D
  $-1 to 1$
Why
$r-squared is a proportion between 0 and 1 (commonly written as a percent 0%-100%).$
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Sample 2difficulty 2/5
$The means of x and y in a sample are 50 and 100. The slope of the least-squares regression line is 1.5.$
$What is the y-intercept?$
- A
  $75$
- B
  $50$
- C
  $150$
- D
  $25$
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Why
$The line passes through (x-bar, y-bar): a = y-bar - b * x-bar = 100 - 1.5(50) = 25.$
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Sample 3difficulty 2/5
$Two models compete: Model A has r-squared = 0.40 and Model B has r-squared = 0.85.$
$Which statement is best supported?$
- A
  $Cannot be compared without more info$
- B
  $Model A is more accurate$
- C
  $The models are equally good$
- D
  $Model B explains more of the variability in y$
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Why
$Higher r-squared indicates a greater proportion of variability in y explained by the linear model.$
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Sample 4difficulty 2/5
$Output is shown for a regression of sales on ad spend.$
$Which is the best interpretation of r-squared?$
- A
  $About 72% of advertisements lead to sales$
- B
  $Sales increase by 72% per ad dollar$
- C
  $The model predicts sales correctly 72% of the time$
- D
  $About 72% of the variation in sales is explained by the linear regression on ad spend$
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Why
$r-squared is the proportion of variability in the response (sales) accounted for by the linear model with the predictor (ad spend).$
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Sample 5difficulty 2/5
$For a linear regression, sx = 4, sy = 10, and r = 0.6.$
$What is the slope of the least-squares regression line predicting y from x?$
- A
  $1.5$
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- B
  $2.4$
- C
  $0.6$
- D
  $0.24$
Why
$Slope b = r * (sy/sx) = 0.6 * (10/4) = 1.5.$
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