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# Coefficients for both simple and multiple regressions

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1. A professor wants to test if the number of sunny days in the week before an exam has an influence on student grades .A sample of 20 is taken and the following regression equation is obtained.

Y = 80 - .5X S b1 = .1

a) Test at a=.05
b) Interpret R2

2. Given the following regression equation for a sample of 30:

Y = 200 + .8X1+2.1X2-4X3 Sb1 = .04 Sb2 =1.5 Sb3= 1.2

a) Test at a= .05 if there exists a relationship between each independent variable and the dependent variable.
b) Interpret the b2 coefficient.

https://brainmass.com/statistics/descriptive-statistics/coefficients-both-simple-multiple-regressions-603000

#### Solution Preview

1. A professor wants to test if the number of sunny days in the week before an exam has an influence on student grades. A sample of 20 is taken and the following regression equation is obtained.

^
Y = 80 - .5X S b1 = .1

a) Test at a=.05
We are testing H0: b1=0 vs. Ha: b1≠0
Test statistic=-0.5/0.1=-5.
P-value=0 from t table with df=20-2=18.
Since p-value<0.05, we ...

#### Solution Summary

The solution give detailed steps on calculating and interpreting coefficients for both simple and multiple regressions.

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