Answer: For each additional year of age, mean predicted price decreases by $2,100 Slope estimates change in mean y per 1-unit change in x: each year older, mean price drops by 2.1 thousand dollars = $2,100.

Which is the correct interpretation of the slope?

Answer: For each additional hour studied, predicted score increases by 3.7 points Slope is the predicted change in y per one-unit increase in x. Here predicted score rises 3.7 points per extra hour.

What does this imply about the test H0: beta = 0?

Answer: Fail to reject H0 at alpha = 0.05; 0 is in the interval Since 0 lies inside the 95% CI, we fail to reject H0: beta = 0 at alpha = 0.05.

AP Statistics · Topic 9.3

Justifying a Claim About the Slope of a Regression Model Practice

Part of Inference for Quantitative Data: Slopes.(UNC-4.J)

Practice questions

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Sample questions

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Sample 1difficulty 2/5
$A regression of car price (thousand $) on age (years) gives slope = -2.1.$
$Best interpretation?$
- A
  $Slope is meaningless if negative$
- B
  $For each additional year of age, mean predicted price decreases by $2,100$
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- C
  $Cars cost $2.1 less per year$
- D
  $For each additional dollar, age decreases 2.1 years$
Why
$Slope estimates change in mean y per 1-unit change in x: each year older, mean price drops by 2.1 thousand dollars = $2,100.$
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Sample 2difficulty 2/5
$Output is shown for predicting test score from hours studied.$
$Which is the correct interpretation of the slope?$
- A
  $For each additional point on the test, hours increase by 3.7$
- B
  $For each additional hour studied, predicted score increases by 3.7 points$
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- C
  $The score is 3.7 when hours = 0$
- D
  $Studying causes a 3.7-point gain$
Why
$Slope is the predicted change in y per one-unit increase in x. Here predicted score rises 3.7 points per extra hour.$
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Sample 3difficulty 3/5
$A 95% confidence interval for the slope of a regression is (-0.5, 2.3).$
$What does this imply about the test H0: beta = 0?$
- A
  $Reject H0$
- B
  $Slope is positive$
- C
  $Fail to reject H0 at alpha = 0.05; 0 is in the interval$
  check_circle
- D
  $Test cannot be performed$
Why
$Since 0 lies inside the 95% CI, we fail to reject H0: beta = 0 at alpha = 0.05.$
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Sample 4difficulty 3/5
$A regression of weight (lb) on height (in) gives slope b = 4.5 with 95% CI (3.0, 6.0).$
$Best interpretation of the CI?$
- A
  $We are 95% confident that for each 1-inch increase in height, the mean weight increases by between 3.0 and 6.0 lb$
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- B
  $Probability the slope is between 3 and 6 is 95%$
- C
  $Slope is exactly 4.5$
- D
  $95% of all individuals weigh between 3 and 6 lb$
Why
$A confidence interval for slope in a regression context refers to mean change in y per unit change in x.$
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Sample 5difficulty 4/5
$A regression yields a tiny slope of 0.005 with p = 0.001 due to large n = 5000.$
$What is the best interpretation?$
- A
  $Cannot be statistically significant$
- B
  $Slope is huge$
- C
  $Sample size is irrelevant$
- D
  $Statistically significant but possibly not practically meaningful$
  check_circle
Why
$Large samples can detect even very small effects as significant. Practical significance must be considered separately from statistical significance.$
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