Statistics Regression & Correlation Analysis 1 — Questions and Answers
Question 1: What does the correlation coefficient r = 0 indicate?
- No linear relationship between the two variables (Correct answer)
- A perfect negative linear relationship
- A perfect positive linear relationship
- A non-linear relationship exists
Correct answer: No linear relationship between the two variables
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?
- The average change in Y for a one-unit increase in X (Correct answer)
- The value of Y when X equals zero
- The correlation between X and Y
- The standard deviation of the residuals
Correct answer: The average change in Y for a one-unit increase in X
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?
- The proportion of variance in Y explained by the regression model (Correct answer)
- The correlation coefficient squared only for perfect fits
- The probability that the regression is significant
- The slope divided by the standard error
Correct answer: The proportion of variance in Y explained by the regression model
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?
- The difference between observed and predicted values (Correct answer)
- The slope of the regression line
- The intercept of the regression equation
- The standard deviation of X
Correct answer: The difference between observed and predicted values
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?
- −1 to +1 (Correct answer)
- 0 to 1
- −∞ to +∞
- 0 to +∞
Correct answer: −1 to +1
Pearson's r is bounded between −1 (perfect negative) and +1 (perfect positive linear relationship).
Question 6: In multiple regression, what does multicollinearity refer to?
- High correlation among predictor variables (Correct answer)
- Non-linear relationship between predictors and outcome
- Unequal variance of residuals
- Outliers in the response variable
Correct answer: High correlation among predictor variables
Multicollinearity occurs when two or more predictor variables are highly correlated, making coefficient estimates unstable.
Statistics Regression & Correlation Analysis 1
What does the correlation coefficient r = 0 indicate?