Statistics Regression & Correlation Analysis

Question 1

What does the correlation coefficient r = 0 indicate?

Accepted Answer

No linear relationship between the two variables

Answer

A correlation of 0 means there is no linear association; a non-linear relationship may still exist.

Question 2

In simple linear regression, what does the slope coefficient represent?

Accepted Answer

The average change in Y for a one-unit increase in X

Answer

The slope (b₁) describes how much the predicted response Y changes on average for each one-unit increase in the predictor X.

Question 3

What does the coefficient of determination R² represent?

Accepted Answer

The proportion of variance in Y explained by the regression model

Answer

R² measures the percentage of total variation in the response variable that is accounted for by the predictor(s).

Question 4

What is a residual in linear regression?

Accepted Answer

The difference between observed and predicted values

Answer

A residual is the observed Y minus the predicted Ŷ, representing unexplained variation.

Question 5

Which of the following is the correct range for the Pearson correlation coefficient r?

Accepted Answer

−1 to +1

Answer

Pearson's r is bounded between −1 (perfect negative) and +1 (perfect positive linear relationship).

Statistics Practice Test