On the basis of the output of autoplot() (assuming that the linearity assumption and constant variance assumption are satisfied) does there seem to be any issues with the normality assumption.

Question

On the basis of the output of autoplot() (assuming that the linearity assumption and constant variance assumption are satisfied) does there seem to be any issues with the normality assumption.

BlackTom AI · Accepted Answer

First, restating the scenario in your own words helps ground the analysis: you’re evaluating autoplot() outputs to judge whether the normality assumption holds, given linearity and constant variance appear satisfied. Now, let's examine each option in turn.
Option 1: 'No, the residual vs. leverage plot is close to flat indicating that there are no issues with the normality assumption.' This is incorrect because the residuals-vs-leverage plot primarily informs about influence and heteroscedasticity concerns, not directly about normality. A flat leverage plot does not provide evidence about normality violations, so this statement misattributes what the plot shows.
Option 2: 'Yes, by looking at the scale-location plot, we see a systematic deviation of the residuals from a flat line, indicating a failure of the normality assumption.' The scale-location (a.k.a. spread vs fitted) plot helps assess homoscedasticity, not normality. A systematic deviation there would suggest issues with constant variance rather than normality, so tying it to normality is incorrect.
Option 3: 'No, there is an increasing trend in the scale-location plot indicating that there are no issues with the normality assumption.' This mixes two ideas: an increasing trend in scale-location suggests changes in variance with fitted values, not evidence of normality. Also, as soon as variance changes with fitted values, that points to heteroscedasticity, which again is not a direct measure of normality, making this assertion inconsistent.
Option 4: 'Yes, by looking at the QQ-plot we see a systematic deviation from the dashed line, indicating a failure of the normality assumption.' The QQ-plot against a theoretical normal distribution is the standard diagnostic for normality. A clear systematic deviation from the reference line (the dashed line) signals departures from normality, which is precisely what this option describes. This aligns with established diagnostic practice.
In summary, options 1 and 2 misidentify which plots diagnose normality versus other assumptions, option 3 incorrectly interprets the scale-location plot and makes a false claim about normality, and option 4 correctly points to the QQ-plot as the normality diagnostic with the expected interpretation of deviation from the line. The reasoning in each choice rests on understanding what each diagnostic plot conveys about model assumptions.

SDS 324E Homework 8

On the basis of the output of autoplot() (assuming that the linearity assumption and constant variance assumption are satisfied) does there seem to be any issues with the normality assumption.

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