Q3.3.2: Model evaluation – coefficient of determination, R-squared

Answer the following questions based on Section 3.3.2: Model evaluation - coefficient of determination, R².

Consider the following data:

X1	0.5	0.9	1.1	1.7	1.5
X2	1.2	0.8	0.6	1.0	1.5
Y	5.9	5.0	5.2	6.5	7.8

Use statistical software to fit a simple linear regression model with response variable, Y, and predictor variables, X1 and X2. 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 is the value of adjusted R²? Write a number rounded to four decimal places.

3.

What does the coefficient of determination, R², represent?

The correlation between Y and the fitted/predicted values from the model.

The sum of squared residuals.

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

The squared estimated standard deviation of the random errors.

4.

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

The same unit as the predictor variables, X1 and X2.

The same unit as the response variable, Y.

The ratio of predictor variable, X1, and predictor variable, X2.

The coefficient of determination is unit-free.

5.

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

True False

6.

True or false? The coefficient of determination, R², is equal to the square of the correlation between Y and the fitted/predicted values from the model.

True False

Applied Regression Modeling

3rd edition

Iain Pardoe