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Basic Linear Regression Model

Given Data:

X Y
11 24
12 25
16 33
13 25
12 19
15 24
16 25
18 35

Use the given data (above) to answer the following questions:

1. Determine the regression equation relating X and Y? Use the formula
to determine the value of and hence find .

2. State the models being compared to determine if there is a linear relationship between Y and X (i.e. model C and model A).

3. State the null and alternative hypotheses for this model comparison.

4. Report a complete ANOVA table for the above model comparison, include R2.

5. Calculate the 95% confidence interval for β1.

6. What are your conclusions based on the significance test from the ANOVA table and the confidence interval.

Solution Preview

Please see the attached file.

1. Determine the regression equation relating X and Y? Use the formula
to determine the value of and hence find .

X Y (X - )2
(Y - )2
(X - )(Y - )2
11 24 9.765625 5.0625 7.03125
12 25 4.515625 1.5625 2.65625
16 33 3.515625 45.5625 12.65625
13 25 1.265625 1.5625 1.40625
12 19 4.515625 52.5625 15.40625
...

Solution Summary

The solution determines a regression equation relating X and Y. The models being compared are determined. A null and alternative hypothesis for this model comparison is given.

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