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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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Rank the correlations Consider each of the following relationships: the heights of fathers and the heights of their adult sons, the heights of husbands and the heights of their wives, and the heights of women at age 4 and their heights at age 18. Rank the correlations Page Number: between these pairs of variables from largest to smallest. Explain your reasoning.
Residual wins Refer to Exercise 37. The Chicago Cubs won the World
Page Number: 203 Series in 2016. They had 103 wins and spent $182 million on the payroll. Calculate and interpret the residual for the Cubs.
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
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?
Drilling down beneath a lake in Alaska yields chemical evidence of past changes in climate. Biological silicon, left by the skeletons of single-celled creatures called diatoms, is a measure of the abundance of life in the lake. A rather complex variable based on the ratio of certain isotopes relative to ocean water gives an indirect measure of moisture, mostly from snow. As we drill down, we look further into the past. Here is a scatterplot of data from 2300 to 12,000 years ago:
a. Identify the unusual point in the scatterplot and estimate its x and y coordinates.
b. Describe the effect this point has on
i. the correlation.
ii. the slope and y-intercept of the least-squares line.
iii. the standard deviation of the residuals.
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