Lecture 35- Prediction from Regression Models Flashcards
What was the first gem about p values?
P values can indicate how incompatible the data are with a specified statistical model
What should we be aware of when using prediction?
Don’t extrapolate too far out. If predicting using a model made from values in a very different part of the scale it doesn’t necessarily hold that the model still holds.
What type of interval do we want to calculate if we are interested in estimating the mean response from data?
Confidence interval : follow standard format of estimate +/- multiplier x standard error
When constructing a confidence interval what distribution will the multiplier come from?
T distribution with 2 degrees of freedom
How do you do prediction for a point? What is this called?
- Sub the predictor variable x into the fitted equation to get the expected y value
- Point estimate
Find the confidence interval for the point estimate 82.98 on slide 679-680
Answers on slides
What are the two sources of error from predicting a response for a new data point?
- Error in the estimate of the mean response causes error
- A new data point will have a response that is distributed with error about its mean value
What is a prediction error?
- Analogous to standard error but takes into account both sources of error when predicting
- There is an extra term in the square root (1) that accounts for variation about the mean
Calculate the prediction interval for at X0=80 on slide 685
answers on slide
What is the difference between a prediction interval and confidence interval?
- For any given value of x of the predictor (y) estimates of the mean response and prediction of response for the data point are the same
- A confidence interval describes precision of estimation of mean response
- A prediction interval describes precision of prediction for the new data point (an individual rather than average).
What is always wider: prediction or confidence intervals?
Prediction, there is more uncertainty
