Confidence and prediction interval

  • Thread starter bizzy
  • Start date
  • #1
1
0
I need help with this question.

Suppose we are making predictions of the dependent variable y for specific values of the independent variable x using a simple linear regression model holding the confidence level constant. Let C.I = the width of the confidence interval for the average value y for a given value of x, and P.I = the width of the prediction interval for a single value y for a given value of x.

I need to know if C.I > P.I., < P.I., = P.I., or = .5 P.I.
 

Answers and Replies

  • #2
statdad
Homework Helper
1,495
36
The length of the confidence interval will always be less than the length of the prediction interval, because the margin of error in the confidence interval is always smaller than the margin of error in the prediction interval.

The length of the confidence interval estimate is twice this:

[tex]
s t \sqrt{\frac 1 n + \frac{(x_0 - \bar x)^2}{\sum (x-\bar x)^2}
[/tex]

the length of the prediction interval estimate is twice this:

[tex]
s t \sqrt{1+ \frac 1 n + \frac{(x_0 - \bar x)^2}{\sum (x-\bar x)^2}
[/tex]

The difference between the two margins of error varies, depending on the sample size, [tex] s [/tex], and the magnitude of the [tex] x [/tex] values. So far as I know, there is no simple rule that always works to quantify the magnitude of the difference.
 

Related Threads on Confidence and prediction interval

  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
2K
Replies
3
Views
1K
Replies
1
Views
3K
Replies
2
Views
1K
  • Last Post
Replies
3
Views
2K
Replies
24
Views
4K
Replies
3
Views
17K
Top