• Find and interpret the confidence interval for the mean response
• Find and interpret the prediction interval for an individual response
• Identify whether a confidence interval or a prediction interval is more appropriate in context of the problem

When fitting a linear regression model, we assume that the distribution of the response variable is approximately normal for a given value of the explanatory variable. It is important for that condition to hold when using prediction intervals, since these intervals take into account the scatter of the points about the line.

We can check that this condition holds by examining the distribution of the residuals. If the distribution of the residuals is approximately normal, we can feel confident that the distribution of the response variable is normally distributed about the regression line for each value of the explanatory variable.

Enter the data set: Capital Bikeshare in Washington D.C. accordingly.

Step 1: Select the Fitted Values and Residual Analysis tab.

Step 2: Select the option “Histogram/Boxplot of Residuals.”

Step 3: Select the option “Superimpose Normal Curve.”

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If the residuals are not normally distributed, you can report the prediction interval with a note indicating that caution should be applied when using the results from the interval.

Notice that we checked the distribution of the residuals when calculating the prediction interval for an individual response, but not for the confidence interval for the mean response. The reliability of the confidence interval for the mean response does not rely on the normality of the distribution of the residual due to the Central Limit Theorem.