A different report card. Refer to Exercise 4.57. Prepare a report card based on the analysis of open space per person that you performed in Exercise 4.59. Write a short paragraph comparing this report card with the one that you prepared in Exercise 4.57. Which do you prefer? Give reasons for your answer.
Exercise 4.57
Open space per person. Refer to Exercises 4.56 to 4.58. Open space in acres per person is an alternative way to report open space. Divide open space by population to compute the value of this variable for each city. Using this new variable as the response variable and population as the explanatory variable, answer the questions given in Exercise 4.56. How do your new results compare with those that you found in that exercise?
Exercises 4.56
Open space and population. The New York City Open Accessible Space Information System Cooperative (OASIS) is an organization of public and private sector representatives that has developed an information system designed to enhance the stewardship of open space.17 Data from the OASIS Web site for 12 large U.S. cities follow. The variables are population in thousands and total park or other open space within city limits in acres.
(a) Make a scatterplot of the data using population as the explanatory variable and open space as the response variable.
(b) Is it reasonable to fit a straight line to these data? Explain your answer.
(c) Find the least-squares regression line. Report the equation of the line and draw the line on your scatterplot
(d) What proportion of the variation in open space is explained by population?
Exercises 4.57
Prepare the report card. Refer to the previous exercise. One way to compare cities with respect to the amount of open space that they have is to compare the actual open space with the open space that is predicted by the least-squares regression line.
Using the data and the regression line from the previous exercise, compute the difference between the actual open space and the predicted open space for each city. Cities with positive differences are doing better than predicted, while those with negative differences are doing worse
Make a table with the city name and the difference, ordered from best to worst by the size of the difference. (In the following section, we will learn more about how to use these differences, which we call "residuals.")