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Statistics: Multiple Regression Analysis

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41. A multiple regression analysis based on n= 24 data points yielded the following fitted model:

Y = 130.0093 - 3.5017 + .0034

The error sum of squares was 465.1348. Each of the following statements is incorrect; your job is to correct each.

a. For each one-unit change in , we expect Y to decrease by -3.5017 units

b. The estimated standard error of the regression is 22.1493

c. There is a direct relation between and Y

d. The fitting error for the data point Y = 50, , and = 1024 is 52.1565

e. If we reduce the value of from 0.0034 to 0.0014, the error sum of squares will
be less than 465.1348

42. Find the cutoff F-value for the following testing situations:

a. Ho: Beta 1 = Beta 2 = Beta 3 = 0; n = 28; and significance level = 0.05

b. Ho: Beta1 = Beta 2 = Beta 3 = Beta 4 = Beta 5 = Beta 6 = 0; n = 35; and significance level = 0.10

c. Ho: Beta 1 = Beta 2 = 0; n = 15; and significance level = 0.01

43, 44. See attached word document.

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41. a. the right statement is:
For each one unit increase in x1, we expect Y to decrease by 3.5017 units.
b. the estimated standard error of the regression ...

Solution Summary

The solution provides a multiple regression analysis for the given data.

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Bio-Statistics: Multiple Regression Analysis

1. Consider the data shown in this table measured in a sample of n=25 undergraduates in an on-campus survey of health behaviors. Enter the data into an excel worksheet for analysis.

2. Estimate the multiple linear regression equation relating number of cups of coffee per week, female gender, and number of hours of exercise per week to GPA (consider GPA the dependent or outcome variable).
Please explain in detail or a summary (roughly 200 words), responding to the questions posed in the problem.

ID AGE FEMALE YEAR IN SCHOOL GPA CURRENT SMOKER EXERCISE PER WEEK (h) AVERAGE DRINKS PER WEEK CUPS OF COFFEE PER WEEK
1 18 1 FR 3.85 1 7 3 3
2 21 0 JR 3.27 1 3 2 4
3 19 1 SO 2.90 0 0 4 7
4 22 0 SR 3.65 1 0 2 4
5 21 1 SR 3.41 1 0 1 3
6 20 0 JR 3.20 0 2 5 8
7 19 1 JR 2.89 1 1 4 10
8 17 0 FR 3.75 0 6 0 0
9 18 0 SO 4.00 0 6 2 6
10 17 1 SO 3.18 0 3 5 7
11 21 0 JR 2.58 1 3 12 12
12 22 1 SR 2.98 0 2 3 4
13 19 0 FR 3.16 1 2 0 6
14 21 1 JR 3.36 1 3 1 2
15 22 1 SO 3.72 0 6 3 0
16 19 0 SO 3.30 1 4 0 6
17 16 0 FR 3.28 0 4 0 5
18 22 0 SR 2.98 0 0 8 5
19 17 1 FR 3.90 0 7 0 2
20 20 1 SR 3.78 1 4 6 2
21 21 1 SO 3.26 1 2 3 4
22 23 0 JR 3.01 0 1 9 7
23 23 0 SR 3.83 1 5 4 4
24 17 1 FR 3.76 0 5 2 1
25 22 1 SR 3.05 0 1 5 5

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