Mathematics, statistics

60. T Drug abuse revisited Chapter 6 0, Exercise 42 D examines results of a survey conducted in the United States and 10 countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. Below is the scatterplot. Summary statistics showed that the mean percent that had used marijuana was 23.9%, with a standard deviation of 15.6%. An average of 11.6% of teens had used other drugs, with a standard deviation of 10.2%. 30.0- 22.5 Other Drugs (%) 15.0 7.5 12.5 25.0 37.5 50.0 Marijuana (%) a. Do you think a linear model is appropriate? Explain. b. For this regression, R" is 87.3%. Interpret this statistic in this context. c. Write the equation you would use to estimate the percentage of teens who use other drugs from the percentage who have used marijuana. d. Explain in context what the slope of this line means. e. Do these results confirm that marijuana is a "gateway drug," that is, that marijuana use leads to the use of other drugs?E. Stopping times Using data from El) compact cars, a consumer group develops a model that predicts the stopping time for a vehicle by using its weight. You consider using this model to predict the stopping time for your large SUV. Explain why this is not advisable. 1E. More residuals Suppose you have t a linear model to some data and now take a look at the residuals. For each of the following possible residuals plots, tell whether you would try a re-expression and. if so. why. 26. Bad model? A student who has created a linear model is disappointed to nd that her R2 value is a very low 13%. a. Does this mean that a linear model is not appropriate? Explain. b. Does this model allow the student to make accurate predictions? Explain