AP Statistics · Topic 9.5

Carrying Out a Test for the Slope of a Regression Model Practice

Part of Inference for Quantitative Data: Slopes.(VAR-7.F)

Practice questions

17

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Sample questions

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Sample 1difficulty 1/5
$A simple linear regression is fit on n = 30 observations.$
$What is df for the t-test on slope?$
- A
  $27$
- B
  $29$
- C
  $30$
- D
  $28$
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Why
$df = n - 2 = 30 - 2 = 28 (estimating intercept and slope).$
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Sample 2difficulty 2/5
$A regression output reports residual df = 17.$
$What is the sample size n?$
- A
  $18$
- B
  $20$
- C
  $19$
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- D
  $17$
Why
$df = n - 2, so n = df + 2 = 17 + 2 = 19.$
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Sample 3difficulty 2/5
$A regression of weekly sales (y, in thousands) on advertising spend (x) gives the output below.$
$What is the estimated slope?$
- A
  $4.80$
- B
  $12.5$
- C
  $2.4$
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- D
  $0.5$
Why
$The slope is the coefficient on x: 2.4. The constant 12.5 is the intercept.$
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Sample 4difficulty 2/5
$The same regression output is shown with slope estimate 2.4 and SE = 0.5.$
$What is the t-statistic for testing H0: beta = 0?$
- A
  $4.80$
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- B
  $12.50$
- C
  $2.40$
- D
  $0.50$
Why
$t = (b - 0)/SE(b) = 2.4/0.5 = 4.80, as shown.$
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Sample 5difficulty 2/5
$Computer output shows slope = 4.2 with SE = 1.4, n = 30.$
$What is the t-statistic?$
- A
  $3.0$
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- B
  $5.6$
- C
  $1.4$
- D
  $2.5$
Why
$t = b / SE(b) = 4.2 / 1.4 = 3.0.$
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