Applied Regression Modeling

3rd edition

Iain Pardoe

A concise, comprehensive treatment of the application of statistical regression analysis suitable for undergraduate and graduate students. Covers simple linear regression, multiple linear regression, model building, and advanced regression topics.

by Iain P
on May 2, 2021

Answer the following questions based on Section 2.3.3: Model evaluation - slope parameter.

Consider the following data:

X 1.1 1.4 1.8 2.5 3.2
Y 3.8 5.7 6.9 8.1 10.0
Use statistical software to fit a simple linear regression model with response variable, Y, and predictor variable, X. 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?

4. 

What is the test conclusion?

5. 

Use the fact that the 97.5th percentile of a t-distribution with 3 degrees of freedom is 3.182 to calculate the lower bound of a 95% confidence interval for the slope, b1. Write a number rounded to three decimal places.

6. 

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

7. 

True or false? The closer the observed Y-values are to their predictions along the fitted regression line, the larger is the absolute value of the test statistic for a two-tail hypothesis test of NH: b1 = 0 versus AH: b1 ≠ 0.

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