Q5.1.2: Influential points – leverage – Applied Regression Modeling, 3rd edition

Answer the following questions based on Section 5.1.2: Influential points - leverage.

Consider the following data:

X	0.8	0.6	0.8	0.2	0.5	1.0	1.5	0.1	0.2	0.5
Y	0.7	0.5	0.5	0.3	0.6	0.9	1.1	0.1	0.4	0.4

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.

What are the estimated intercept and slope for this fitted model?

Intercept: 0.1440; slope: 0.6605.

Intercept: 0.6605; slope: 0.1440.

Intercept: 0.6418; slope: 0.1521.

Intercept: 0.1521; slope: 0.6418.

2.

Which observation has the highest leverage for this fitted model?

X = 0.1, Y = 0.1.

X = 0.5, Y = 0.6.

X = 0.8, Y = 0.5.

X = 1.5, Y = 1.1.

3.

Obtain the leverage for this observation. Round your answer to 2 decimal places.

4.

Remove this observation from the dataset and refit the simple linear regression model with response variable, Y, and predictor variable, X. What are the estimated intercept and slope for this refitted model?

Intercept: 0.1440; slope: 0.6605.

Intercept: 0.6605; slope: 0.1440.

Intercept: 0.6418; slope: 0.1521.

Intercept: 0.1521; slope: 0.6418.

5.

True or false? The observation with the highest leverage has a relatively large influence on the results as removing it from the dataset causes a relatively large change in the estimated regression line.

True False

X	0.8	0.6	0.8	0.2	0.5	1.0	1.5	0.1	0.2	0.5
Y	0.7	0.5	0.5	0.3	0.6	0.9	1.1	0.1	0.4	0.4

X	0.8	0.6	0.8	0.2	0.5	1.0	1.5	0.1	0.2	0.5
Y	0.7	0.5	0.5	0.3	0.6	0.9	1.1	0.1	0.4	0.4

Applied Regression Modeling

3rd edition

Iain Pardoe

X	0.8	0.6	0.8	0.2	0.5	1.0	1.5	0.1	0.2	0.5
Y	0.7	0.5	0.5	0.3	0.6	0.9	1.1	0.1	0.4	0.4