Problem 6
A student who has created a linear model is disappointed to find that her \(R^{2}\) 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.
Problem 15
Suppose a researcher studying health issues measures blood pressure and the percentage of body fat for several adult males and finds a strong positive association. Describe three different possible causeand-effect relationships that might be present.
Problem 16
A researcher studying violent behavior in elementary school children asks the children's parents how much time each child spends playing computer games and has their teachers rate each child on the level of aggressiveness they display while playing with other children. Suppose that the researcher finds a moderately strong positive correlation. Describe three different possible cause-and-effect explanations for this relationship.
Problem 21
Here's a plot showing the federal rate on 3 -month Treasury bills from 1950 to 1980 , and a regression model fit to the relationship between the Rate (in \%) and Years since 1950 (www.gpoaccess.gov/eop/). Dependent variable is: Rate R-squared \(=77.4 \% \quad s=1.239\) \(\begin{array}{ll}\text { Variable } & \text { Coefficient } \\ & 0.640282\end{array}\) \(\begin{array}{ll}\text { Intercept } & \text { u.to } 40 \\\ \text { Year }-1950 & 0.247637\end{array}\) a) What is the correlation between Rate and Year? b) Interpret the slope and intercept. c) What does this model predict for the interest rate in the year \(2000 ?\) d) Would you expect this prediction to have been accurate? Explain.
Problem 25
For women, pregnancy lasts about 9 months. In other species of animals, the length of time from conception to birth varies. Is there any evidence that the gestation period is related to the animal's lifespan? The first scatterplot shows Gestation Period (in days) vs. Life Expectancy (in years) for 18 species of mammals. The highlighted point at the far right represents humans. a) For these data, \(r=0.54\), not a very strong relationship. Do you think the association would be stronger or weaker if humans were removed? Explain. b) Is there reasonable justification for removing humans from the data set? Explain. c) Here are the scatterplot and regression analysis for the 17 nonhuman species. Comment on the strength of the association. d) Interpret the slope of the line. e) Some species of monkeys have a life expectancy of about 20 years. Estimate the expected gestation period of one of these monkeys.
