Writing Projects

Writing Projects

Question 6.100

1. Choose two variables that you think have a roughly straight-line relationship. Gather data on these variables and do a statistical analysis: Make a scatterplot, find the correlation, find the regression line (use a graphing calculator or software), and draw the line on your plot. Then write a short report on your work. Some examples of suitable pairs of variables are as follows:

  1. The height and arm span of a group of people
  2. The height and walking stride length of a group of people
  3. The price per ounce and bottle size in ounces for several brands of shampoo and several bottle sizes for each brand
  4. The weight and fuel efficiency of motor vehicles [Google “vehicle weight” for lists of weights of specific vehicles, then look up the fuel efficiency (pick among city, highway, or combined mpg) of the particular vehicles.]

Question 6.101

2. Can regression help protect voting rights? This example is adapted from FAPP author Lawrence Lesser’s work as a statistician for the Texas Legislative Council. To comply with the Voting Rights Act, a state cannot redraw its districts in a way that dilutes the voting strength of a protected group. Because we cannot know how individuals voted, we cannot directly measure if minority and majority persons tend to prefer different candidates. Although there are technical details and assumptions we cannot fully discuss here, you can begin to understand how voting preference might be estimated by exploring the following dataset for nine equal-sized districts, where is the percentage of voters who are Hispanic and is the percentage of voters that voted for the candidate preferred by most Hispanics:

14 7 19 27 37 36 53 48 65
12 18 24 36 42 53 68 79 86
District 1 2 3 4 5 6 7 8 9

290

  1. Produce a scatterplot, correlation value, and regression equation. Describe the relationship between the concentration of Hispanic population and the proportion of votes that went to the Hispanic-preferred candidate.
  2. Give a practical interpretation of the value of the slope coefficient. Give a practical interpretation of the value of that would be predicted when and when .

Question 6.102

3. Spotlight 6.3 (page 260) discussed Sir Francis Galton’s study of the heights of men and their fathers. In this writing assignment, you will adapt his study to students. In order to do so, you will need to collect the following data from one or two classes:

  • Have male students record their heights and the heights of their fathers.
  • Have female students record their heights and the heights of their mothers.
  1. Using parent’s height as the explanatory variable, make two scatterplots, one for the males and the other for the females. Find the correlations between parent’s height and student’s height for males and females. Compare the patterns in the two scatterplots for form, strength, and direction.

  2. Discuss the following algebraic representation of regression to the mean for males and females:

  3. Determine the equations for the least-squares regression lines for predicting student’s height from parent’s height. Compare and interpret the slopes of your two lines.

Question 6.103

4.Table 5.13 (page 226) contains data on baseball players ranked in the top 100 in terms of career batting averages. Exercises 9 and 10 in Chapter 5 and Exercise 60 in Chapter 6 were based on these data. Write a report based on your analysis of these data. Feel free to include analysis of other data that can be found at www.baseball-reference.com/. (You will need to use technology—graphing calculators, spreadsheet, or statistical software—for this project.)