(a)
Draw the scatter diagram that shows the relationship between television and overweight.
(a)
Explanation of Solution
Figure 1 shows the scatter diagram of television and overweight.
In the above figure, the vertical axis measures overweight and the horizontal axis measures television. The position of the scatters shows a positive relationship between overweight and television.
Scatter diagram: The scatter diagram shows the value of two variables plotted along two axes. Each scatter represents the relationship between the variables.
(b)
Calculate the least squares line and interpret the slope of the line.
(b)
Explanation of Solution
The least squares regression line is shown below:
Where b0 is the y-intercept and b1 is the slope of the regression line.
The least squares regression line is calculated as follows:
Table 1
Xi | Yi | Xi2 | Yi2 | XiYI | |
1 | 42 | 18 | 1,764 | 324 | 756 |
2 | 34 | 6 | 1,156 | 36 | 204 |
3 | 25 | 0 | 625 | 0 | 0 |
4 | 35 | –1 | 1,225 | 1 | –35 |
5 | 37 | 13 | 1,369 | 169 | 481 |
6 | 38 | 14 | 1,444 | 196 | 532 |
7 | 31 | 7 | 961 | 49 | 217 |
8 | 33 | 7 | 1,089 | 49 | 231 |
9 | 19 | –9 | 361 | 81 | –171 |
10 | 29 | 8 | 841 | 64 | 232 |
11 | 38 | 8 | 1,444 | 64 | 304 |
12 | 28 | 5 | 784 | 25 | 140 |
13 | 29 | 3 | 841 | 9 | 87 |
14 | 36 | 14 | 1,296 | 196 | 504 |
15 | 18 | –7 | 324 | 49 | –126 |
Total | 472 | 86 | 15,524 | 1,312 | 3,356 |
These table values are obtained using a spreadsheet.
The least square line shows that weight increases on average by 0.9675 pounds for each additional hours of television.
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Chapter 16 Solutions
Statistics for Management and Economics (Book Only)
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