By Duane C. Hinders — McGraw-Hill Professional

Updated on Feb 4, 2011

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

### Problems

- 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*H*_{0}:*b*= 0 has the same value as the*t*-test statistic for*H*_{0}:*r*= 0. - The
*t*-test for the slope of a regression line is always two sided (*H*_{A}: β ≠ 0).

- I only
- II only
- III only
- I and II only
- I and III only

- In the computer output for regression,
- The value of the
*t*-test statistic for*H*_{0}: β = 0 is- 4.05
- –1.72
- 0.4925
- 6.143
- 0.0802

- 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 (
*s*_{b})? - 17033.53
- 6953.91
- 2206.98
- 9225.16 ± 17033.53
- 3115.84
- 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,*s*= 0.11. Determine a 95% confidence interval for the slope of the regression line._{b}- 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.

### Solutions

- 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
*H*: 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._{A} - 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.

From 5 Steps to a 5 AP Statistics. Copyright © 2010 by The McGraw-Hill Companies. All Rights Reserved.

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