Q2.3.2: Model evaluation – coefficient of determination, R-squared

Answer the following questions based on Section 2.3.2: Model evaluation - coefficient of determination, R².

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 coefficient of determination, R²? Write a number rounded to four decimal places.

2.

What does the coefficient of determination, R², represent?

The proportion of variation in X accounted for by the fitted model.

The proportion of variation in Y accounted for by the fitted model.

The estimated slope of the regression line.

The correlation between X and Y.

3.

What is the unit of measurement of the coefficient of determination, R²?

The coefficient of determination 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.

True or false? The closer the observed Y-values are to their predictions along the fitted regression line, the larger is the coefficient of determination, R².

True False

5.

True or false? The coefficient of determination, R², is positive if X and Y are positively correlated or negative if X and Y are negatively correlated.

True False

Applied Regression Modeling

3rd edition

Iain Pardoe