STAT1008 Lecture Notes - Lecture 34: Thai Poetry, Body Fat Percentage, Prediction Interval
STAT1008 Week 12 Lecture A
● Inference for Regression Predictions:
○ For a single predictor model and a particular value (x*) of the predictor, the
predicted response (Y) is: y hat = b0 + b1x*
○ How accurate is the prediction?
■ Two forms:
● Confidence interval for mean Y
● Prediction interval for individual Y’s
● CI and PI for regression:
○ CI for mean Y tries to capture the “true” line for the population
○ Prediction interval for individual Y’s tries to capture the data points in the
population
○ How much might the fitted line vary from sample to sample?
■ DO THIS BY BOOTSTRAP!
■ Bootstrap regression lines
● Technology for regression intervals:
○ We generally use stat software to provide the CI for regression predictions
● CI for Mean Y at each x*:
○ Trying to capture the line
○ Not individual data values
○ CI gets wider for more extreme predictor values
○ At the extreme ends the CI gets wider from the regression line that is to
accommodate the variability of X itself. Thus used to control the variability of X
○ What about capturing individual values?
● Prediction interval for individual Y:
○ Need to account for the random variability (error) around the line
○ Epsilon ~ N(0, sigma2)
● PI for final when x* = 90:
○ If the mean square error is small then the intervals are small
● Body fat percentage
○ One of the following is a CI for the mean value and the other is a prediction
interval for individual values, both for predicting the body fat percentage for a
male with an abdominal circumference of 90cm. Which is the confidence
interval?
■ Since CI is always narrower pick the narrower option hence A
○ What is the prediction interval?
■ PI is always the wider interval hence A
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