12.4 For each of the following, explain what is wrong and why. (a) (1m) A 95%...
12.4 For each of the following, explain what is wrong and why.
(a) (1m) A 95% confidence interval for the mean response is the same width regardless of the value of x.
(b) (1m) To test H0: b1 = 0, use a t test.
(c) (1m) For a particular value of the explanatory variable x, the confidence interval for the mean response will be wider than the prediction interval for a future observation
Homework Answers
(a) (1m) A 95% confidence interval for the mean response is the same width regardless of the value of x.
In this statement the wrong part is that interval is same as width but it is not true, width changes with respect to value of x.
(b) (1m) To test H0: b1 = 0, use a t test.
Here in order to test the slope of regression we want to use a t-statistic
with (b1- hypothesized value) / SE(b1).
(c) (1m) For a particular value of the explanatory variable x, the confidence interval for the mean response will be wider than the prediction interval for a future observation.
The prediction interval is always wider than the confidence interval of the mean response because of the added uncertainty involved in predicting a single response versus the mean response.
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12.4 For each of the following, explain what is wrong and
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