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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

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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