(a)
Draw the scatter diagram.
(a)
Explanation of Solution
Figure 1 shows the scatter diagram of Y and X.
In the above figure, the position of the scatters shows a positive relationship between variables Y and X.
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 linear relationship.
(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 | XiY1 | |
1 | 3 | 25 | 9 | 625 | 75 |
2 | 5 | 110 | 25 | 12100 | 550 |
3 | 2 | 9 | 4 | 81 | 18 |
4 | 6 | 250 | 36 | 62500 | 1500 |
5 | 1 | 3 | 1 | 9 | 3 |
6 | 4 | 71 | 16 | 5041 | 284 |
Total | 21 | 468 | 91 | 80,356 | 2,430 |
These table values are obtained using a spreadsheet.
This calculation is enough evidence to conclude that variables X and Y are in a linear relationship.
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Chapter 16 Solutions
Statistics for Management and Economics (Book Only)
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