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Inference for Regression Multiple Choice Practice Problems for AP Statistics

By — McGraw-Hill Professional
Updated on Feb 4, 2011

Review the following concepts if necessary:

Problems

  1. Which of the following statements is (are) true?
    1. In the computer output for regression, s is the estimator of σ, the standard deviation of the residuals.
    2. The t-test statistic for the H0: b = 0 has the same value as the t-test statistic for H0: r = 0.
    3. The t-test for the slope of a regression line is always two sided (HA: β ≠ 0).
    1. I only
    2. II only
    3. III only
    4. I and II only
    5. I and III only
  2. Use the following output in answering questions 2–4:

    A study attempted to establish a linear relationship between IQ score and musical aptitude. The following table is a partial printout of the regression analysis and is based on a sample of 20 individuals.

  3. The value of the t-test statistic for H0: β = 0 is
    1. 4.05
    2. –1.72
    3. 0.4925
    4. 6.143
    5. 0.0802
  4. A 99% confidence interval for the slope of the regression line is
    1. 0.4925 ± 2.878(6.143)
    2. 0.4925 ± 2.861(0.1215)
    3. 0.4925 ± 2.861(6.143)
    4. 0.4925 ± 2.845(0.1215)
    5. 0.4925 ± 2.878(0.1215)
  5. Which of the following best interprets the slope of the regression line?
    1. For each increase of one IQ point, the Musical Aptitude score increases by 0.4925 points.
    2. As IQ score increases, so does the Musical Aptitude score.
    3. For each increase of one IQ point, the Musical Aptitude score is predicted to increase by 0.4925 points.
    4. For each additional point of Musical Aptitude, IQ is predicted to increase by 0.4925 points.
    5. There is a strong predictive linear relationship between IQ score and Musical Aptitude.
  6. The two screens shown below were taken from a: TI-83/84 LinRegTTest. What is the standard error of the slope of the regression line (sb)?
    1. 17033.53
    2. 6953.91
    3. 2206.98
    4. 9225.16 ± 17033.53
    5. 3115.84
  7. A group of 12 students take both the SAT Math and the SAT Verbal. The least-squares regression line for predicting Verbal Score from Math Score is determined to be Verbal Score = 106.56 + 0.74(Math Score). Further, sb = 0.11. Determine a 95% confidence interval for the slope of the regression line.
    1. 0.74 ± 0.245
    2. 0.74 ± 0.242
    3. 0.74 ± 0.240
    4. 0.74 ± 0.071
    5. 0.74 ± 0.199

Solutions

  1. The correct answer is (d). II is true since it can be shown that . III is not true since, although we often use the alternative HA: β ≠ 0, we can certainly test a null with an alternative that states that there is a positive or a negative association between the variables.
  2. The correct answer is (a). .
  3. The correct answer is (e). For n = 20, df = 20 – 2 = 18 t* = 2.878 for C = 0.99.
  4. The correct answer is (c). Note that (a) is not correct since it doesn't have "predicted" or "on average" to qualify the increase. (b) Is a true statement but is not the best interpretation of the slope. (d) Has mixed up the response and explanatory variables. (e) Is also true (t = 4.05 P-value = 0.0008) but is not an interpretation of the slope.
  5. The correct answer is (c). The TI-83/84 does not give the standard error of the slope directly. However,
  6. The correct answer is (a). A 95% confidence interval at 12 – 2 = 10 degrees of freedom has a critical value of t* = 2.228 (from Table B; if you have a TI-84 with the invT function, invT(0.975,10)= 2.228). The required interval is 0.74 ± (2.228)(0.11) = 0.74 ± 0.245.
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