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Describe the effect (if any) on the width (difference between the upper and lower endpoints) of a prediction interval if all else remains the same...
1. Describe the effect (if any) on the width (difference between the upper and lower endpoints) of a prediction interval if all else remains the same except:
- the sample size is increased.
- the variability in the values of the predictor variable increases.
- the variability in the values of the response variable increases.
- the value of interest for the predictor variable moves further from the mean value of the predictor variable.
2.Suppose a linear model is fit to predict Y = weight using X = height. If instead a new linear model is fitusing Y = height and X = weight (i.e, reversing X and Y) state whether each of the following would be thesame for this new model as it was for the original model, or if it would be different.
a. The values of the sample slope and intercept.
b. The value of r^2.
c. The residuals for each person.
d. The value of the F statistic for testing H0: β1 = 0.
