Question

(4 points) 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. 1. Plot A shows that A. The relationship between x and y cannot be assumed to be linear. B. The residuals do not appear to be normally distributed. C. No assumptions have been violated. D. The data does not appear to be from independent observations. E. The variability of points around the least-squares line is not roughly constant. 2. Plot B shows that A. No assumptions have been violated. B. The residuals do not appear to be normally distributed. C. The data does not appear to be from independent observations. D. The relationship between x and y cannot be assumed to be linear. E. The variability of points around the least-squares line is not roughly constant. 3. Plot C shows that A. The relationship between x and y cannot be assumed to be linear. B. The data does not appear to be from independent observations. C. The residuals do not appear to be normally distributed. D. The variability of points around the least-squares line is not roughly constant. E. No assumptions have been violated. 4. Plot D shows that A. The variability of points around the least-squares line is not roughly constant. B. No assumptions have been violated. C. The data does not appear to be from independent observations. D. The residuals do not appear to be normally distributed. E. The relationship between x and y cannot be assumed to be linear.

Answer 1

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ANSWER:

1. Plot A shows a fairly random pattern and hence,

No assumption has been violated.

Option B is correct.

2. Plot B shows a specific type of cluster pattern which indicates that the variability is not constant.

Option D is correct.

3. Plot C shows a nonlinear pattern.

Option B is correct.

4. Plot D shows a lot of overlapping of points which indicates that the data does not appear to be from independent observations.

Option E is correct.

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