Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 282The value of t* comes from the t-distribution with n−2 degrees of freedom.The prediction interval holds for all x simultaneously. It is often plotted using twolines on the scatterplot to show the upper and lower limits.The predict () function will return the lower and upper endpoints for each value of thepredictor. We specify interval="prediction" (which can be shortened) and a confidencelevel with level=. (The default is 0.95.)For the heart-rate example we have:> pred.res = predict(res, int = "pred")> pred.resfit lwr upr1 193.2 185.0 201.42 189.4 181.3 197.5...A matrix is returned with columns giving the data we want. We cannot access these withthe data frame notation pred. res$lwr, as the return value is not a data frame. Rather wecan access the columns by name, like pred. res [, ’lwr’ ] or by column number, as in> pred.res[,2] # the ’lwr’ column1 2 3 4 5 6 7 8 910185.0 181.3 177.6 173.9 170.1 166.3 162.4 158.5 154.6185.0...We want to plot both the lower and upper limits. In our example, we have the predictedvalues for the given values of age. As the age variable is not sorted, simply plotting willmake a real mess. To remedy this, we specify the values of the age variable for which wemake a prediction. We use the values sort (unique (age)), which gives just the x values inincreasing order.> age.sort = sort(unique(age))> pred.res = predict(res.mhr, newdata = data.frame(age= age.sort),+ int="pred")> pred.res[,2]1 2 3 4 5 6 7 8 9185.0 181.3 177.6 173.9 170.1 166.3 162.4 158.5 154.6Now we can add the prediction intervals to the scatterplot with the lines() function(matlines () offers a one-step alternative). The result is Figure 10.7.> plot(mhr ~ age); abline(res)> lines(age.sort,pred.res[,2] , lty=2) # lower curve> lines(age.sort,pred.res[,3], lty=2) # upper curve