1. Business Statistics - QBM117
Using the regression equation for prediction

2. Objectives
To calculate the prediction interval for a particular value of y.
To calculate the confidence interval estimator of the expected value of y.
To test for a significant linear correlation.

3. Using our linear model for prediction
Once we have determined that a linear model is appropriate for our data set, we can use it to predict values of the dependent variable.
We would like to know the uncertainty in our prediction.
This can be determined by calculating
a prediction interval for a particular value of y;
a confidence interval estimator of the expected value of y.

4. The prediction interval of a particular value of y
This interval is used when we want to predict one particular value of the dependent variable (y), for a specific value of the independent variable.
The prediction interval for a particular value of y is
where
is the given value for x and

5. The confidence interval estimator of the expected value of y
This interval is used when we want to predict the mean value of y, for a specific value of the independent variable.
The confidence interval for the mean value of y is
where
is the given value for x and

6. How do these two intervals differ?
The confidence interval of the expected value of y is narrower than the prediction interval for a particular value of y.
This is because, individual observations are more variable than the average of a population of values.

7. Example
Predict with 95% confidence the salary of Jennifer, who has 10 years experience.
The prediction interval for a particular value of y is

8. The prediction interval for a particular value of y is

9. The prediction interval for a particular value of y is

10. Therefore Jennifer, with 10 years experience would have a salary of between $12 340 and $51 700.

11. Example
Estimate with 95% confidence the expected salary of people with 10 years experience.
The confidence interval for the expected value of y is

12. Therefore the average salary of all people with 10 years experience would be between $ and $

13. Exercises to be completed before next lecture
S&S
( abridged)
Exam revision to be completed before next lecture
Print off a copy of the Spring 2002 exam and attempt question 1 and questions 1-5 of the multiple choice questions.