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# Multiple Regression -- SAS Output

I have never used SAS before, but I need to answer some multiple regression problems using SAS output.

Please see the attached files. Please label the variable used in answering the question so I can understand what is done.

For a sample of people, three measurements are taken on each person (skin, thigh, arm) in an attempt to obtain variables useful in predicting their body fat (also measured). Output of SAS regression of fat on skin, thigh, and arm variables and regression of fat on skin are given on the following pages.

1. Given a formula(s) to construct a confidence interval for &#61538;0+50&#61538;1+20&#61538;2+30&#61538;3. Make it clear that you could calculate the lower and upper bounds if asked. Include the Student's t value for a 95% confidence level.

2. The regression coefficient associated with skin differs in the full and simple linear regression models. Explain the difference.

3. There are 10 confidence intervals in the middle of page D. What confidence level can be associated with the claim that all 10 are correct inferences?

#### Solution Preview

For a sample of people, three measurements are taken on each person (skin, thigh, arm) in an attempt to obtain variables useful in predicting their body fat (also measured). Output of SAS regression of fat on skin, thigh, and arm variables and regression of fat on skin are given on the following pages.

1. Given a formula(s) to construct a confidence interval for &#61538;0+50&#61538;1+20&#61538;2+30&#61538;3. Make it clear that you could calculate the lower and upper bounds if asked. Include the Student's t value for a 95% confidence level.

You said that you only needed help with 2 out of the 3 questions. Consider the next two my official answers. I think I can help you with this one, but I'm not 100% on it.

The estimate of &#61538;0+50&#61538;1+20&#61538;2+30&#61538;3 can be calculated by plugging in the estimates of &#61538;0-3 (from the top of page D), then multiplying and adding:

(-67.35) + 50(2.04) + 20(-1.35) + 30(0.60) = -67.35 + 102 - 27 + 18 = 25.65

To make a confidence interval, we need to ...

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