Question
In: Statistics and Probability
The following bivariate data set contains an outlier. x y 28.5 59.3 -6.4 -356.8 29.7 81.6...
The following bivariate data set contains an outlier.
| x | y |
|---|---|
| 28.5 | 59.3 |
| -6.4 | -356.8 |
| 29.7 | 81.6 |
| 23.9 | 1298 |
| 23.4 | 1724.5 |
| -11.9 | 303 |
| 12.3 | -810.6 |
| 46.3 | -628.5 |
| 24.7 | 1557.2 |
| 14.4 | 394.8 |
| 7.8 | -1789.2 |
| 6 | -1949.6 |
| 30.8 | 2369.6 |
| 28.5 | 1974.8 |
| 220.9 | 37.7 |
What is the correlation coefficient with the
outlier?
rw =
What is the correlation coefficient without the
outlier?
rwo =
Would inclusion of the outlier change the evidence for or against a
significant linear correlation?
- Yes. Including the outlier changes the evidence regarding a linear correlation.
- No. Including the outlier does not change the evidence regarding a linear correlation.
Question for thought: Would you always draw the same conclusion
with the addition of an outlier?
Solutions
Expert Solution
Correlation coefficient with the outlier rw = 0.0553
For finding out outlier, we need to plot scatter plot.
From the scatter plot be can seen that point x = 220 and Y = 37.7 is an outlier.
Correlation coefficient with the outlier rwo = 0.3799
We can seen that rwo = 0.3799 is quite greater than rw = 0.0553. Thus, it can be inferred that including the outlier changes the evidence regarding a linear correlation.
Yes. Including the outlier changes the evidence regarding a linear correlation.
We can not always draw the same conclusion with the addition of an outlier. This is because sample size also impacts the effect of the outliers. The smaller the sample size, the greater the effect of the outlier. At some point when the sample size is fairly large, the outlier will have little or no effect on the size of the correlation coefficient.
orchestra answered 2 years agoRelated Solutions
The following bivariate data set contains an outlier. x y 47.6 53.7 40.6 112.6 28.9 72.2...
The following bivariate data set contains an outlier.
x
y
47.6
53.7
40.6
112.6
28.9
72.2
36.1
101.1
32.4
112.4
26.8
67.1
36.8
38.9
33.1
70.1
67.5
8.6
43.3
-6.4
50.1
41.3
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3.2
29.8
41.7
55
-32.8
189.6
548.8
What is the correlation coefficient with the
outlier?
rw =
What is the correlation coefficient without the
outlier?
rwo =
Would inclusion of the outlier change the evidence for or against a
significant linear correlation at 5% significance?
A) No....
The following bivariate data set contains an outlier. x y 89.1 -294.6 75.3 273.5 90.4 -222.1...
The following bivariate data set contains an outlier.
x y
89.1 -294.6
75.3 273.5
90.4 -222.1
79.9 111.5
80.5 685.1
84.7 -193.8
67.6 -259.6
84.5 559.5
73.4 521.2
87.7 -444
91.2 -303.4
87.5 642
72.8 -25.8
67.6 530.6
162 315.7
What is the correlation coefficient with the outlier?
rw =
What is the correlation coefficient without the outlier?
rwo =
Would inclusion of the outlier change the evidence for or against a
significant linear correlation?
No. Including the outlier does...
The following bivariate data set contains an outlier. x y 12.9 79.8 51.9 77.6 26.3 66.5...
The following bivariate data set contains an outlier.
x
y
12.9
79.8
51.9
77.6
26.3
66.5
-5.1
82.9
47
65.4
19.7
75.9
16.7
78.4
2.1
77.1
21.5
74.5
46.2
57.3
35.1
65.4
83.5
38.9
51.1
61.7
15.2
89.3
349.3
240.5
What is the correlation coefficient with the
outlier?
rw =
What is the correlation coefficient without the
outlier?
rwo =
Would inclusion of the outlier change the evidence for or against a
significant linear correlation at 5% significance?
No. Including...
the following bivariate data set contains an outlier. x y 27.7 12.9 29 13.9 33.1 7.6...
the following bivariate data set contains an outlier.
x
y
27.7
12.9
29
13.9
33.1
7.6
31.7
48.2
32.3
12.4
31.1
32.9
29
22.4
35.2
29.5
47.2
62.3
31.7
21.9
27.6
20.4
29.2
16.9
37.6
54.2
34.1
27.7
106
-156.5
What is the correlation coefficient with the
outlier?
rw =
What is the correlation coefficient without the
outlier?
rwo =
The following bivariate data set contains an outlier. x y 62.8 256.5 61.9 -39.3 47.2 765.4...
The following bivariate data set contains an outlier.
x
y
62.8
256.5
61.9
-39.3
47.2
765.4
54.3
1350.5
72.5
479.2
84.7
2508.9
43.9
-2120.9
54
-1687.9
45.6
1021.6
68.5
786.7
34.7
-4360.1
51.3
-1825.9
50.7
-1365.3
77
488.1
234.7
-236
What is the correlation coefficient with the
outlier?
rw =
What is the correlation coefficient without the
outlier?
rwo =
Would inclusion of the outlier change the evidence for or against a
significant linear correlation?
No. Including the outlier does...
The following bivariate data set contains an outlier. x y 44.3 187 58.2 239.6 42 341.2...
The following bivariate data set contains an outlier.
x
y
44.3
187
58.2
239.6
42
341.2
42.4
-358.8
47.9
-347.1
47.8
103
55
95.5
47.4
-146.3
31.9
698.6
68.2
-477.3
52.6
-363.4
63.1
569.2
56
-203.7
74.8
545.3
203.5
4226.3
What is the correlation coefficient with the
outlier?
rw =
What is the correlation coefficient without the
outlier?
rwo =
Would inclusion of the outlier change the evidence for or against a
significant linear correlation?
Yes. Including the outlier changes...
The following bivariate data set contains an outlier. x y 53.3 151.7 37.1 -307.3 44.6 -469.7...
The following bivariate data set contains an outlier.
x
y
53.3
151.7
37.1
-307.3
44.6
-469.7
47
-475.2
68.4
292.5
50.3
383.5
55.7
-1180.8
30.7
223.7
60.6
-600.8
39.9
-152.6
49.3
-335.2
50.1
590.1
54.9
99
63.1
243.5
181.5
-6493.5
What is the correlation coefficient with the
outlier?
rw = (Round to three decimal
places)
What is the correlation coefficient without the
outlier?
rwo = (Round to three decimal
places)
a) Run a regression analysis on the following bivariate set of data with y as the...
a) Run a regression analysis on the following bivariate set of
data with y as the response variable.
x
y
10.7
81.6
13.7
81.5
36.7
56.5
4
72.1
50.7
23.2
47.6
-4.8
37.3
31.9
24.3
75.2
21.5
59.3
17.2
54.6
23.6
75.5
22.2
60.8
29.3
51
14
63.4
0.2
102.7
30.7
48.2
10.3
74.8
26.5
48.2
23.1
87
Verify that the correlation is significant at an ?=0.05?=0.05.
If the correlation is indeed significant, predict what value (on
average) for the...
Calculate the sample covariance of the following bivariate data set. X Y 27 5 15 6...
Calculate the sample covariance of the following bivariate data
set. X Y 27 5 15 6 12 -2 b. Calculate the coefficient of
correlation of the data set. c. Describe in words the information
given to us by the sample covariance and by the sample correlation.
Explain how the correlation gives us more precise information.
8. Run a regression analysis on the following bivariate set of data with y as the...
8. Run a regression analysis on the following bivariate set of
data with y as the response variable.
x
y
27.2
68.2
28.1
66.7
28.7
64.6
30.2
66.4
33.7
69.5
31.8
68.3
30.4
67.8
28.6
65.5
32.5
69.4
34.8
67.9
33.3
67.1
28
66.1
- Find the correlation coefficient and report it accurate to
three decimal places.
r =
- What proportion of the variation in y can be
explained by the variation in the values of x? Report
answer...
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