# simple linear regression in matrix terms assignment

## STA 9700: Homework 6

As with the previous assignment, this is a first draft of a section of your semester project.

Lecture Notes 6 **The Matrix Approach to Regression**

- Simple Linear Regression in Matrix Terms

In this exercise, you will **use the matrix approach to do a simple linear regression of y on x** for just one of your x-variables. Use a modest subset of rows, say, n=8, which is the sample size I used in the Excel example.

(a) Show the X matrix using your x-variable and the necessary column of 1's.

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(b) Show the y-vector, composed of your observed y-values.

(c) In Excel, use matrix operations to compute the b-vector, Hat matrix, and the y-hat vector. Show your Excel work, using the posted Excel file as a guide.

(d) Using **R or Proc Reg**, run the regression of y on x and show the output. Check that the b-vector agrees with the values found using the matrix approach in Excel. If the values do not agree, remain calm. Just state, "There was a problem," and go on. You can fix it, later.

(e) On page 7 of STA 9700 Lecture Notes 6, it is shown that for **simple regression** we can compute the entries of the hat matrix directly from the data. Compute the value of h2,3 by the method shown, and check your result matches the value in the Excel hat matrix in the second row, third column. If the result does not match, don't drive yourself crazy: double-check your work once, and then just say, "There was a problem" and go on.

## Multiple Linear Regression in Matrix Terms

In this exercise, add a second regressor variable to the data set used above.

(a) Show the new X matrix.

(b) Use R or SAS Proc IML to fit the model, following the example given in the Lecture Notes (which is also contained in the posted SAS example file). Show the output of that program.

(c) Using Proc Reg in SAS, check the values in the Proc IML b-vector. If the output does not match, just say so. We will get it corrected, later!

```
(d) Show the Proc IML program you used.
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Our **Statistics online help experts** did this assignment initially for another student, and the following attached solution was provided. If you need help the same or a similar project then do not hesitate to contact us.

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