Inference for Regression Free Response 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
1–5. The following table gives the ages in months of a sample of children and their mean height (in inches) at that age.
- Find the correlation coefficient and the least-squares regression line for predicting height (in inches) from age (in months).
- Draw a scatterplot of the data and the LSRL on the plot. Does the line appear to be a good model for the data?
- Construct a residual plot for the data. Does the line still appear to be a good model for the data?
- Use your LSRL to predict the height of a child of 35 months. How confident should you be in this prediction?
- Interpret the slope of the regression line found in question #1 in the context of the problem.
- In 2002, there were 23 states in which more than 50% of high school graduates took the SAT test. The following printout gives the regression analysis for predicting SAT Math from SAT Verbal from these 23 states.
- What is the equation of the least-squares regression line for predicting Math SAT score from Verbal SAT score?
- Interpret the slope of the regression line and interpret in the context of the problem.
- Identify the standard error of the slope of the regression line and interpret it in the context of the problem.
- Identify the standard error of the residuals and interpret it in the context of the problem.
- Assuming that the conditions needed for doing inference for regression are present, what are the hypotheses being tested in this problem, what test statistic is used in the analysis, what is its value, and what conclusion would you make concerning the hypothesis?
- For the regression analysis of question #6:
- Construct and interpret a 95% confidence interval for the true slope of the regression line.
- Explain what is meant by "95% confidence interval" in the context of the problem.
- It has been argued that the average score on the SAT test drops as more students take the test (nationally, about 46% of graduating students took the SAT). The following data are the Minitab output for predicting SAT Math score from the percentage taking the test (PCT) for each of the 50 states. Assuming that the conditions for doing inference for regression are met, test the hypothesis that scores decline as the proportion of students taking the test rises. That is, test to determine if the slope of the regression line is negative. Test at the 0.01 level of significance.
- Some bored researchers got the idea that they could predict a person's pulse rate from his or her height (earlier studies had shown a very weak linear relationship between pulse rate and weight). They collected data on 20 college-age women. The following table is part of the Minitab output of their findings.
- Determine the t-ratio and the P-value for the test.
- Construct a 99% confidence interval for the slope of the regression line used to predict pulse rate from height.
- Do you think there is a predictive linear relationship between height and pulse rate? Explain.
- Suppose the researcher was hoping to show that there was a positive linear relationship between pulse rate and height. Are the t-ratio and P-value the same as in Part (a)? If not, what are they?
- The following table gives the number of manatees killed by powerboats along the Florida coast in the years 1977 to 1990, along with the number of powerboat registrations (in thousands) during those years (we saw the printout for these data in a Cumulative Review Problem in Chapter 9):
- Test the hypothesis that there is a positive linear relationship between the number of powerboat registrations and the number of manatees killed by powerboats. Assume that the conditions needed to do inference for regression have been met.
- Use a residual plot to assess the appropriateness of the model.
- Construct and interpret a 90% confidence interval for the true slope of the regression line (that is, find a 90% confidence interval for the predicted number of additional manatees killed for each additional registered powerboat).