• 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 the objective is to estimate the mean value of the response variable for a particular value of the explanatory variable, [latex]x_0[/latex], we will calculate a confidence interval for the mean response. This interval gives us a range of plausible values the mean value of the response variable takes when [latex]x=x_0[/latex].

We can interpret the [latex]C\%[/latex] confidence interval for the mean response interval as follows:
We are [latex]C\%[/latex] confident that the mean response when the explanatory variable equals [latex]x_0[/latex] is between (lower bound) and (upper bound).

Data set: Capital Bikeshare in Washington D.C.

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When the objective is to predict the value of the response variable for an individual observation with the explanatory variable equal to [latex]x_0[/latex], we will calculate a [latex]C\%[/latex] prediction interval for an individual response, where [latex]x_0[/latex] is the confidence level. This interval gives us a range of plausible values of the response when an individual observation has a value of the explanatory variable equal to [latex]x_0[/latex].

We can interpret the [latex]C\%[/latex] prediction interval for an individual response interval as follows:
We are [latex]C\%[/latex] confident that the value of the response variable for an individual with a value of the explanatory variable equal to [latex]x_0[/latex] is between (lower bound) and (upper bound).

When calculating the prediction interval for an individual observation, we have to take into account two sources of variability (i.e., the reasons our point estimates or predictions may not be exactly right). These are sources of variability due to: (1) the individual values that vary around the population regression line and (2) the fact that we don’t have the equation of the population regression line and must rely on estimates of the slope and intercept.