Which of the following statements is true about prediction intervals and confide
ID: 3259315 • Letter: W
Question
Which of the following statements is true about prediction intervals and confidence intervals for Y in simple linear regression?
A 95% prediction interval for Y given a specific value of the X variable in a regression model is calculated using the formula
A prediction interval gives a range of "reasonable" values for an actual (new) value of the Y variable, given a specific choice of the X variable, while a confidence interval gives a range of "reasonable values" for the mean of the Y variable, given a specific choice of the X variable.
A prediction interval gives a range of "reasonable" values for the actual (new) value of the Y variable, given a specific choice of the X variable. It will, in general, always be narrower than a confidence interval for the mean value of the Y variable because it is easier in general to predict a specific value than to estimate a mean.
A prediction interval gives a range of "reasonable" values for the mean value of the Y variable, given a specific choice of the X variable, while a confidence interval gives a range of "reasonable values" for an actual (new) value of the Y variable, given a specific choice of the X variable.
If a 95% prediction interval contains 0, we will be able to reject the hypothesis at the 0.05 level of significance.
A 95% prediction interval for Y given a specific value of the X variable in a regression model is calculated using the formula
,
where s is the sample standard deviation, is the sample mean, and n is the sample size. A confidence interval for the mean value of Yreplaces the value of "2" with 1.96.
A prediction interval gives a range of "reasonable" values for an actual (new) value of the Y variable, given a specific choice of the X variable, while a confidence interval gives a range of "reasonable values" for the mean of the Y variable, given a specific choice of the X variable.
A prediction interval gives a range of "reasonable" values for the actual (new) value of the Y variable, given a specific choice of the X variable. It will, in general, always be narrower than a confidence interval for the mean value of the Y variable because it is easier in general to predict a specific value than to estimate a mean.
A prediction interval gives a range of "reasonable" values for the mean value of the Y variable, given a specific choice of the X variable, while a confidence interval gives a range of "reasonable values" for an actual (new) value of the Y variable, given a specific choice of the X variable.
Explanation / Answer
Answer
Option 3.)
A prediction interval gives a range of "reasonable" values for an actual (new) value of the Y variable , given a specific choice of the X variable. While a confidence interval gives a range of "reasonable values" for the mean of the Y variable given a specific choice of the X variable.
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