Question

A random sample of 214 junior and senior college students was taken. Each student reported the average amount of sleep they get per night (in minutes) and their current college GPA. Plots from a simple linear regression analysis are displayed below.   

GPA versus Sleep 5.0 college GPA 3.5 2.0 100 700 200 300 400 500 600 average sleep (minutes/day) Residual Plot 2.0 residuals (min) 0.5 -1.0 100 700 200 300 400 500 600 average sleep (minutes/day) Normal Probability Plot of Residuals Sample Quantiles OOOOOO -1.0 0.0 1.0 2.0 3 -2 -1 0 1 2 3 Theoretical Quantiles

Which of the following is true about the linearity condition?

1.The linearity condition is not satisfied because there is curvature in the normal probability plot of the residuals.

2.The linearity condition is satisfied because most of the residuals fall on or near the reference line in the normal probability plot of the residuals.

3. The linearity condition is satisfied because there is no curvature in the scatterplot.

4. The linearity condition is not satisfied because there is a point with an unusually large residual in the residual plot.

There is one student who reported a college GPA over 5.0. Which of the following is the most appropriate action to take first?

1. Remove the outlier as it is influential on the analysis.

2. Remove the outlier since it’s impossible to have a GPA over 5.

3. Do an analysis with and without the outlier and report both.

4. Determine if the person with the GPA over 5 is from a different population.

Which of the following is true regarding the constant variation condition?

1.The constant variation condition is not met since not all of the residuals fall on the reference line in the normal probability plot.

2.The constant variation is met since most of the residuals fall on or near the reference line in the normal probability plot.

3.The constant variation condition is satisfied since there is not curvature of the residuals in the residual plot.

4.The constant variation condition is not satisfied since the variation of the residuals in the residual plot is more in the middle of the plot than at either end of the plot.

Which of the following is true about the normality condition?

1. The residuals are approximately normally distributed since the residuals fall on or near the reference line in the normal probability plot, except for a few at either end of the plot.

2. The residuals are not normally distributed since most of the residuals do not fall on the reference line in the residual plot.

3. The residuals are approximately normally distributed since they are equally spaced above and below the reference line in the residual plot.

4. Since there is a linear relationship between the response and explanatory variables, the normality condition is automatically satisfied.

Since there is a linear relationship between the response and explanatory variables, the constant variation condition is automatically satisfied.

Answer 1

Which of the following is true about the linearity condition?

Answer:

4. The linearity condition is not satisfied because there is a point with an unusually large residual in the residual plot.

Explanation:

From the residual plot, we can see an outlier data point with unusually high value and since the regression analysis is highly sensitive to an outlier, the linearity condition is not satisfied

There is one student who reported a college GPA over 5.0. Which of the following is the most appropriate action to take first?

Answer:

2. Remove the outlier since it’s impossible to have a GPA of over 5.

Explanation:

Since the GPA is measured on a scale from 0 to 5, it will be considered as an invalid data point.

Which of the following is true regarding the constant variation condition?

Answer:

3. The constant variation condition is satisfied since there is no curvature of the residuals in the residual plot.

Explanation:

The residual plot draws the scatterplot between the residual values and the y value. If the constant variance holds, the data values should be distributed randomly along the horizontal line without any distinct pattern. From the given plot we can not see any distinct pattern which means the error variance is constant hence there is no violation of constant variance assumption.

Which of the following is true about the normality condition?

Answer:
3. The residuals are approximately normally distributed since they are equally spaced above and below the reference line in the residual plot.

Explanation:

The normal probability plot for the residuals is used to see whether the distribution of data points is approximately normal such that if the normality assumption holds, the data points should lie along the straight line, From the given plot we can see that the data points are along the reference line hence the normality assumption is met.