Inference for Regression Multiple Choice Practice Problems for AP Statistics
Review the following concepts if necessary:
- Simple Linear Regression for AP Statistics
- Inference for the Slope of a Regression Line for AP Statistics
- Confidence Interval for the Slope of a Regression Line for AP Statistics
- Inference for Regression Using Technology for AP Statistics
- Which of the following statements is (are) true?
- In the computer output for regression, s is the estimator of σ, the standard deviation of the residuals.
- The t-test statistic for the H0: b = 0 has the same value as the t-test statistic for H0: r = 0.
- The t-test for the slope of a regression line is always two sided (HA: β ≠ 0).
- I only
- II only
- III only
- I and II only
- I and III only
- The value of the t-test statistic for H0: β = 0 is
- A 99% confidence interval for the slope of the regression line is
- 0.4925 ± 2.878(6.143)
- 0.4925 ± 2.861(0.1215)
- 0.4925 ± 2.861(6.143)
- 0.4925 ± 2.845(0.1215)
- 0.4925 ± 2.878(0.1215)
- Which of the following best interprets the slope of the regression line?
- For each increase of one IQ point, the Musical Aptitude score increases by 0.4925 points.
- As IQ score increases, so does the Musical Aptitude score.
- For each increase of one IQ point, the Musical Aptitude score is predicted to increase by 0.4925 points.
- For each additional point of Musical Aptitude, IQ is predicted to increase by 0.4925 points.
- There is a strong predictive linear relationship between IQ score and Musical Aptitude.
- 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)?
- 9225.16 ± 17033.53
- 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.
- 0.74 ± 0.245
- 0.74 ± 0.242
- 0.74 ± 0.240
- 0.74 ± 0.071
- 0.74 ± 0.199
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.
- 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.
- The correct answer is (a). .
- The correct answer is (e). For n = 20, df = 20 – 2 = 18 t* = 2.878 for C = 0.99.
- 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.
- The correct answer is (c). The TI-83/84 does not give the standard error of the slope directly. However,
- 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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