A residual plot from a simple linear regression analysis is shown to the right.

Question

A residual plot from a simple linear regression analysis is shown to the right. Use the plot to answer the question below. A scatterplot has a horizontal axis labeled x and a vertical axis labeled residuals. A horizontal line segment starts at the vertical axis at a vertical coordinate of 0 and passes through a series of 27 plotted points. The points are spread across the line in such a way that the scattering of the points about the line is very minimal at the left end of the horizontal line, increases as the value of x approaches the middle of the horizontal axis and decreases as the value of x increases beyond the middle value to a minimum at the right end of the horizontal line. Which of the following statements regarding the plot is true? A. The condition that the residuals have constant variation is not met since the variation increases and then decreases as x gets larger. B. The condition that the residuals are normally distributed is not met since there is a diamond shape to the residuals in the residual plot. C. The condition that the residuals have constant variation is met since the lines connecting the largest positive residuals and largest negative residuals are parallel. D. The condition that the residuals are normally distributed is not met since not all of the residuals fall on the reference line in the residual plot.

Explanation / Answer

Answer (A) The condition that the residuals have constant variation is not met since the variation increases and then decreases as x gets larger.

Reason it would have had constant variance or variation if the residuals were scattered randomly around zero. But here it first increases and then decreases indicating the variation is not constant.

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