Q3.3.5: Model evaluation – individual parameter tests – Applied Regression Modeling, 3rd edition

Answer the following questions based on Section 3.3.5: Model evaluation - regression parameters - individual tests.

Consider the following data:

X₁	0.5	0.8	1.0	1.7	1.4	1.3	1.8	1.2	1.1	0.9
X₂	0.7	0.4	0.3	0.2	1.0	0.6	0.5	0.4	0.8	0.9
X₃	0.5	0.4	0.3	0.9	0.6	0.8	0.8	0.5	0.9	0.7

Use statistical software to fit a multiple linear regression model with response variable, Y, and predictor variables, X₁, X₂, and X₃. Use the fitted model to answer the following questions.

1.

Calculate the t-test statistic for a two-tail hypothesis test of NH: b₁ = 0 versus AH: b₁ ≠ 0. Write a number rounded to three decimal places.

2.

What is the p-value for the test? Write a number rounded to three decimal places.

3.

What is the test decision based on a significance level = 0.05?

Reject NH in favor of AH since the p-value < 0.05.

Reject NH in favor of AH since the p-value > 0.05.

Fail to reject NH since the p-value < 0.05.

Fail to reject NH since the p-value > 0.05.

4.

What is the test conclusion?

We have insufficient evidence that b1 = 0.

We have insufficient evidence that b1 ≠ 0.

The sample data favor b1 = 0.

The sample data favor b1 ≠ 0.

5.

What is another way of stating the test conclusion?

The sample data suggest that X1 is linearly associated with the response variable.

The sample data suggest that X1 is linearly associated with the response variable, after controlling for X2 and X3.

The sample data suggest that X1 is not linearly associated with the response variable.

The sample data suggest that X1 is not linearly associated with the response variable, after controlling for X2 and X3.

6.

Use the fact that the 97.5^th percentile of a t-distribution with 6 degrees of freedom is 2.447 to calculate the lower bound of a 95% confidence interval for the parameter, b₁. Write a number rounded to three decimal places.

7.

Calculate the upper bound of a 95% confidence interval for the parameter, b₁. Write a number rounded to three decimal places.

Applied Regression Modeling

3rd edition

Iain Pardoe