Given are data for two variables, x and y.
xi
6
11
15
18
20
yi
6
8
13
20
30
(a)
Develop an estimated regression equation for these data. (Round your numerical values to two decimal places.)
Å· = -6.93 + 1.60x
(b)
Compute the residuals. (Round your answers to two decimal places.)
xi
yi
Residuals
6
6
0.40
11
8
-0.80
15
13
-0.20
18
20
1.20
20
30
7.20
(c)
Develop a plot of the residuals against the independent variable x.
A residual plot has 5 points plotted on it. The horizontal axis ranges from 0 to 25 and is labeled: x. The vertical axis ranges from -6 to 6 and is labeled: Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. 2 points lie above the line and 3 lie below it. The points are plotted from left to right in a downward, diagonal direction starting from the upper left corner of the plot. The maximum residual is located at x = 6 and the minimum occurs at x = 20.
(d)
Compute the standardized residuals. (Round your answers to two decimal places.)
xi
yi
Standardized Residuals
6
6
0.11
11
8
-0.22
15
13
-0.06
18
20
0.33
20
30
1.99
(e)
Develop a plot of the standardized residuals against Å·.
A standardized residual plot has 5 points plotted on it. The horizontal axis ranges from 0 to 30 and is labeled: Å·. The vertical axis ranges from -3 to 3 and is labeled: Standardized Residuals. There is a horizontal line that spans the graph at 0 on the vertical axis. 2 points lie above the line and 3 lie below it. The points start above the line at about Å· = 3 in the upper left corner of the plot, then are plotted from left to right in a downward, diagonal direction until reaching a low below the line at about Å· = 17. They then continue to be plotted in an upward diagonal direction until reaching a high above the line at about Å· = 25.