Q2.3.1: Model evaluation – regression standard error – Applied Regression Modeling, 3rd edition

Answer the following questions based on Section 2.3.1: Model evaluation - regression standard error.

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.

What is the regression standard error, s? Write a number rounded to four decimal places.

2.

What does the regression standard error represent?

The sum of squared residuals.

The estimated standard deviation of the intercept.

The estimated standard deviation of the slope.

The estimated standard deviation of the random errors.

3.

What is the unit of measurement of the regression standard error?

The regression standard error is unit-free.

The same unit as the predictor variable, X.

The same unit as the response variable, Y.

The ratio of the response variable, Y, and the predictor variable, X.

4.

How can we use the regression standard error to assess prediction uncertainty?

Approximately 95% of observed Y-values lie within s of their predictions.

Approximately 95% of observed Y-values lie within 2s of their predictions.

Approximately 95% of observed Y-values are at least s away from their predictions.

Approximately 95% of observed Y-values are at least 2s away from their predictions.

5.

True or false? The closer the observed Y-values are to their predictions along the fitted regression line, the larger is the regression standard error.

True False

Applied Regression Modeling

3rd edition

Iain Pardoe