Residuals vs fitted plots can be used to assess whether the four key assumptions for a simple linear regression have been met. Each of the plots below displays an instance where at least one of these assumptions may not have been met. For each plot, identify which assumption has been most violated, if any.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Residuals vs fitted plots can be used to assess whether the four key assumptions for a simple linear regression have been met. Each of the plots below displays an instance where at least one of these assumptions may not have been met. For each plot, identify which assumption has been most violated, if any.

2.8
3.0
3.2
3.4
3.6
3.8
Fitted value
2.
? v 2.
-10
-5
5
10
A. The data does not appear to be from independent observations.
Fitted value
B. No assumptions have been violated.
C. The relationship between x and y cannot be assumed to be linear.
D. The variability of points around the least-squares line is not roughly constant.
? v 3.
-0.4
-0.2
0.0
0.2
0.4
Fitted value
Residual
-0.5
0'0
S'O
Transcribed Image Text:2.8 3.0 3.2 3.4 3.6 3.8 Fitted value 2. ? v 2. -10 -5 5 10 A. The data does not appear to be from independent observations. Fitted value B. No assumptions have been violated. C. The relationship between x and y cannot be assumed to be linear. D. The variability of points around the least-squares line is not roughly constant. ? v 3. -0.4 -0.2 0.0 0.2 0.4 Fitted value Residual -0.5 0'0 S'O
-0.4
-0.2
0.0
0.2
0.4
Fitted value
20
-10
-5
10
Fitted value
OL
Residual
4.
Transcribed Image Text:-0.4 -0.2 0.0 0.2 0.4 Fitted value 20 -10 -5 10 Fitted value OL Residual 4.
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