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Chapter 3: Q.57 (page 193)
57. Bird colonies Refer to Exercises and . For the regression you performed earlier, and . Explain what each of these values means in this setting.
The values are expected to differ by about from the actual values.
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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?
The scatter plots
Describe the direction of the relationship. Explain why this makes sense
How sensitive to changes in water temperature are coral reefs? To find out, measure the growth of corals in aquariums where the water temperature is controlled at different levels. Growth is measured by weighing the coral before and after the experiment. What are the explanatory and response variables? Are they categorical or quantitative?
How much gas? In Exercise (page ), we examined the relationship between the average monthly temperature and the amount of natural gas consumed in Joan鈥檚 midwestern home. The 铿乬ure below shows the original scatterplot with the least-squares line added. The equation of the least-squares line is
(a) Identify the slope of the line and explain what it means in this setting.
(b) Identify the y-intercept of the line. Explain why it鈥檚 risky to use this value as a prediction.
(c) Use the regression line to predict the amount of natural gas Joan will use in a month with an average temperature of 掳贵.
What鈥檚 my grade? In Professor Friedman鈥檚 economics course, the correlation between the students鈥� total scores prior to the final examination and their final-examination scores is The pre-exam totals for all students in the course have mean and standard deviation The
final-exam scores have mean and standard deviation Professor Friedman has lost Julie鈥檚 final exam but knows that her total before the exam was He decides to predict her final-exam score from her pre-exam total.
(a) Find the equation for the appropriate least-squares regression line for Professor Friedman鈥檚 prediction. Interpret the slope of this line in context.
(b) Use the regression line to predict Julie鈥檚 final exam score.
(c) Julie doesn鈥檛 think this method accurately predicts how well she did on the final exam. Determine Use this result to argue that her actual score could have been much higher (or much lower) than the predicted value.
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