Stat 2118 – Homework 5
Answer the following questions by hand, using matrices.
| X1 | X2 | Y |
| -2 | 1 | 0 |
| -1 | 1 | 1 |
| 0 | 0 | 3 |
| 1 | 1 | 5 |
| 2 | 0 | 6 |
We are interested in fitting the following regression model:
This can also be written in matrix form as
Calculate and
Verify that
Do this my multiplying it by and verifying that the product is , the identity matrix.
Calculate , and write down the least squares function.
Use the least squares function to calculate the predicted values and the residuals.
Calculate SSE, SSTO, SSR, and summarize the results in the ANOVA table.
Perform the Global ANOVA -Test to see if the model is useful.
Calculate and the adjusted .
Calculate s, an estimator of , the standard deviation of .
Calculate a 95% confidence interval for the mean of when and .
Calculate a 95% prediction interval for an individual new value of when and .
Calculate the variance-covariance matrix of .
Perform a -test to see if the term is useful in this model.
Perform a -test to see if the term is useful in this model.
Which model do you think would be best: a simple linear regression with as the predictor variable, a simple linear regression with as the predictor variable, or the first-order multiple regression model with both and ?
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