A statistical program is recommended. You may need to use the
appropriate appendix table or technology to
answer this question.
Data for two
variables, x and y, follow.
xi
1
2
3
4
5
yi
3
7
5
11
14
(a)
Develop the estimated regression equation for these data. (Round
your numerical values to two decimal places.)
? =
(b)
Plot the standardized residuals versus ?.
A
standardized residual plot is labeled y hat on the horizontal axis
and ranges from 0 to 20. The vertical axis is labeled Standardized
Residual and ranges from ?2 to 2. There is a horizontal dashed
line that goes through 0 on the vertical axis. 5 points appear on
the plot at the following approximate locations:
(2.8, 0.7),
(5.4, 0.5),
(8.0, ?0.3),
(10.6, 0.5),
(13.2, ?0.1).
A
standardized residual plot is labeled y hat on the horizontal axis
and ranges from 0 to 20. The vertical axis is labeled Standardized
Residual and ranges from ?2 to 2. There is a horizontal dashed
line that goes through 0 on the vertical axis. 5 points appear on
the plot at the following approximate locations:
(2.8, 0.2),
(5.4, 0.9),
(8.0, ?1.6),
(10.6, 0.2),
(13.2, 0.6).
A
standardized residual plot is labeled y hat on the horizontal axis
and ranges from 0 to 20. The vertical axis is labeled Standardized
Residual and ranges from ?2 to 2. There is a horizontal dashed
line that goes through 0 on the vertical axis. 5 points appear on
the plot at the following approximate locations:
(2.8, 0.9),
(5.4, 0.6),
(8.0, 0.2),
(10.6, 0.2),
(13.2, ?1.6).
A
standardized residual plot is labeled y hat on the horizontal axis
and ranges from 0 to 20. The vertical axis is labeled Standardized
Residual and ranges from ?2 to 2. There is a horizontal dashed
line that goes through 0 on the vertical axis. 5 points appear on
the plot at the following approximate locations:
(2.8, ?1.6),
(5.4, 0.2),
(8.0, 0.2),
(10.6, 0.6),
(13.2, 0.9).
Do there appear to be any outliers in these data? Explain.
The value of the standardized residual
for ---Select--- no observations one
observation two observations three observations four
observations all observations is either greater than +2
or less than ?2. Therefore,
there ---Select--- are no outliers is one
outlier are two outliers are three outliers are four
outliers are five outliers .
(c)
Compute the studentized deleted residuals for these data. (Round
your answers to two decimal places.)
xi
yi
Studentized
Deleted Residual
1
3
2
7
3
5
4
11
5
14
At the 0.05 level of significance, can any of these observations
be classified as an outlier? Explain. (Select all that apply.)
Observation xi = 1 can be
classified as an outlier since it has a large studentized deleted
residual (greater than t0.025 or less
than ?t0.025).Observation xi =
2 can be classified as an outlier since it has a large studentized
deleted residual (greater
than t0.025 or less
than ?t0.025).Observation xi =
3 can be classified as an outlier since it has a large studentized
deleted residual (greater
than t0.025 or less
than ?t0.025).Observation xi =
4 can be classified as an outlier since it has a large studentized
deleted residual (greater
than t0.025 or less
than ?t0.025).Observation xi =
5 can be classified as an outlier since it has a large studentized
deleted residual (greater
than t0.025 or less
than ?t0.025).None of the observations can
be classified as outliers since they do not have large studentized
deleted residuals (greater
than t0.025 or less
than ?t0.025).