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Chapter 3: Q. 55 (page 193)

55. Bird colonies Refer to Exercise 53.
(a) Use your calculator to make a residual plot. Describe what this graph tells you about how well the line fits the data.
(b) Which point has the largest residual? Explain what this residual means in context.

Short Answer

Expert verified

(a) The data does not appear to have any distinct patterns, and the regression line looks to be a good fit for the data.

(b) The largest residual point is(66,6)

Step by step solution

01

Part (a) Step 1: Given information

By using the calculator to make a residual plot. To plot a graph to check the line fits the data.

02

Part (a) Step 2: Explanation

Residuals are on the vertical axis and percent returns are on the horizontal axis, representing the difference between actual and expected levels.

In other words, there does not appear to be any distinctive pattern in the data, and the regression line appears to fit the data nicely.

03

Part (b) Step 1: Concept introduction

The residual value refers to the part of the variability in a dependent variable fragment that remains after the forecasters have taken account of the variability described in the study.

04

Part (b) Step 2: Explanation 

Predicted values and residuals are presented in the table as follows:

Percent return (X)
New adults (Y)
Predicted Y (Y)
Residuals (Y-Y)
74
5
9.43656125
-4.43656125
66
6
11.86874481
-5.868744811
81
8
7.308400634
0.691599366
52
11
16.12506604
-5.125066043
73
12
9.740584195
2.259415805
62
15
13.08483659
1.915163409
52
16
16.12506604
-0.125066043
45
17
18.25322666
-1.253226659
62
18
13.08483659
4.915163409
46
18
17.94920371
0.050796287
60
19
13.69288248
5.307117518
46
20
17.94920371
2.050796287
38
20
20.38138727
-0.381387275

Due to its large deviation from a line, the point (66,6)has the largest residuals. This makes it an outlier in the above table.

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