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Chapter 3: Q. 36 (page 191)
An eccentric professor believes that a child with an IQ should have a reading test score and that the reading score should increase by a point for every additional point of IQ. What is the equation of the professor鈥檚 regression line for predicting reading scores from IQ?
The equation is.
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What affects correlation? Make a scatterplot of the following data:
The correlation for these data is . What is responsible for reducing the correlation to this value despite a strong straight-line relationship between and in most of the observations?
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?
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.
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.
Joan is concerned about the amount of energy she uses to heat her home. The graph below plots the mean number of cubic feet of gas per day that Joan used each month against the average temperature that month (in degrees Fahrenheit) for one heating season.
(a) Does the plot show a positive or negative association between the variables? Why does this make sense?
(b) What is the form of the relationship? Is it very strong? Explain your answers.
(c) Explain what the point at the bottom right of the plot represents.
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