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Chapter 3: Q.30 (page 163)
If women always married men who were years older than themselves, what would the correlation between the ages of husband and wife be?
(a) (c) (e) Can鈥檛 tell without
(b) (d) seeing the data
The correlation between the ages of husband and wife be .
The answer is Option (b)
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Bird colonies Return to the data of Exercise on sparrow hawk colonies. We鈥檒l use these data to illustrate influence.
(a) Make a scatterplot of the data suitable for predicting new adults from the percent of returning adults. Then add two new points. Point A: return,
new adults. Point B: return, new adults. In which direction is each new point an outlier?
(b) Add three least-squares regression lines to your plot: for the original colonies, for the original colonies plus Point , and for the original colonies
plus Point Which new point is more influential for the regression line? Explain in simple language why each new point moves the line in the way your graph shows.
Data on dating A student wonders if tall women tend to date taller men than do short women. She measures herself, her dormitory roommate, and the women in the adjoining rooms. Then she measures the next man each woman dates. Here are the data (heights in inches):
(a) Make a scatterplot of these data. Based on the scatterplot, do you expect the correlation to be positive or negative? Near or not?
(b) Find the correlation r step-by-step. First, find the mean and standard deviation of each variable. Then find the six standardized values for each variable. Finally, use the formula for . Do the data show that taller women tend to date taller men?
Outsourcing by airlines Exercise (page ) gives data for airlines on the percent of major maintenance outsourced and the percent of flight delays blamed on the airline.
(a) Make a scatterplot with outsourcing percent as and delay percent as Hawaiian Airlines is a high outlier in the direction. Because several other airlines have similar values of the influence of this outlier is unclear without actual calculation.
(b) Find the correlation with and without Hawaiian Airlines. How influential is the outlier for correlation?
(c) Find the least-squares line for predicting from with and without Hawaiian Airlines. Draw both lines on your scatterplot. Use both lines to predict the percent of delays blamed on an airline that has outsourced of its major maintenance. How influential is the outlier for the least-squares line?
A data set included the number of people per television set and the number of people per physician for countries. The Fathom screenshot below displays a scatterplot of the data with the least-squares regression line added. In Ethiopia, there were people per TV and people per doctor. What effect would remove this point have on the regression line?
(a) Slope would increase; intercept would increase.
(b) Slope would increase; intercept would decrease.
(c) Slope would decrease; intercept would increase.
(d) Slope would decrease; intercept would decrease.
(e) Slope and intercept would stay the same.
Should you use this line to predict the rat鈥檚 weight at age years? Use the equation to make the prediction and think about the reasonableness of the result. (There aregrams in a pound.)
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