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Chapter 3: Q 32. (page 175)
If women always married men who were 2 years older than themselves, what would be the correlation between the ages of husband and wife?
a. 2
b. 1
c. 0.5
d. 0
e. Can鈥檛 tell without seeing the data
The correct option is (b)
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Stand mixers The scatterplot shows the weight (in pounds) and cost (in dollars) of 11 stand mixers.35 The mixer from Walmart (highlighted in red) was much lighter鈥攁nd cheaper than the other mixers.
a. Describe what influence the highlighted point has on the equation of the least-squares regression line.
b. Describe what influence the highlighted point has on the standard deviation of the residuals and r2
More long jumps Refer to Exercise 52. Use technology to create a residual plot. Sketch the residual plot and explain what information it provides.
Fruit fly thorax lengths (2.2) Fruit flies are used frequently in genetic research because of their quick reproductive cycle. The length of the thorax (in millimeters) for male fruit flies is approximately Normally distributed with a mean of 0.80 mm and a standard deviation of 0.08 mm.21
a. What proportion of male fruit flies have a thorax length greater than 1 mm?
b. What is the 30th percentile for male fruit fly thorax lengths?
The stock market Some people think that the behavior of the stock market in January predicts its behavior for the rest of the year. Take the explanatory variable x to be the percent change in a stock market index in January and the response variable y to be the change in the index for the entire year. We expect a positive correlation between x and y because the change during January contributes to the full year鈥檚 change. Calculation from data for an 18-year period gives x =
(a) Find the equation of the least-squares line for predicting full-year change from January change. Show your work.
(b) The mean change in January is . Use your regression line to predict the change in the index in a year in which the index rises in January. Why could you have given this result (up to roundoff error) without doing the calculation?
Longer strides In Exercise 43, we summarized the relationship between x =
height of a student (in inches) and y = number of steps required to walk the length of a school hallway, with the regression line y^=113.6鈭�0.921x. For this
model, technology gives s = 3.50 and r2 = 0.399.
a. Interpret the value of s.
b. Interpret the value of r2.
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