Based on the residual plot from a simple linear regression analysis below, which
ID: 3128685 • Letter: B
Question
Based on the residual plot from a simple linear regression analysis below, which of the statements following the plot is true? Choose the correct answer below. The condition that the residuals have constant variation is not met since the lines connecting the largest positive residuals and largest negative residuals are not parallel. 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. The condition that the residuals are normally distributed is not met since there is a funnel shape to the residuals in the residual plot. The condition that the residuals have constant variation is met since the lines connecting the largest positive residuals and largest negative residuals are parallel.Explanation / Answer
D is the correct answer.
here we can see that residuals have constant variation above and below the line
The Mean and Standard Deviation of the Residuals
It can be shown that for every set of data, there are two restrictions on the values of the residuals.
ei = 0 and xiei = 0
we see that the mean of the residuals,xiei equals 0 for every set of data. In
symbols, this is a very important equation. Similar to my feelings about
ei = 0 means that the regression line passes through the center of the data in
the sense that: some cases are above the line and some are below, but the sum of the distances
above the line cancel exactly the sum of the distances below the line.
Now that we know the center—mean—of the distribution of the residuals, as in Chapter 1 we
turn to the determination of the amount of spread.
for each xi in the data set, we compared it, via subtraction, to its mean in order to obtain its deviation: (xi mean(x)). Residual ei
is its Thus, the sum of squared deviations of the residuals is simply the sum of squared residuals, which we denote by SSE:
SSE =(ei)^2
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