Free Correlation and Regression MCQs with Answers

• A. Average difference
• B. Absolute magnitudes
• C. Linear association
• D. Percentage change

Explanation: Correlation measures the direction and strength of a linear relationship between two variables.

• A. -1 and 1
• B. 0 and 1
• C. - infinity and infinity
• D. -100 and 100

Explanation: Pearson's correlation coefficient ranges from -1 to +1. A value of +1 or -1 indicates perfect linear association, while 0 indicates no…

• A. Strong and positive
• B. Strong and negative
• C. Weak and positive
• D. Weak and negative

Explanation: The magnitude 0.85 shows a strong relationship, while the negative sign shows that the variables move in opposite directions.

• A. X and Y have no relationship of any kind
• B. The means of X and Y are equal
• C. X and Y have no linear relationship
• D. The variances of X and Y are zero

Explanation: A zero Pearson correlation means that no linear relationship is detected.

• A. Replacing one variable by its square
• B. Adding random error to one variable
• C. Adding a constant to one variable
• D. Removing observations selectively

Explanation: Adding a constant shifts the location of a variable but does not change its pattern of variation with the other variable.

• A. Intercept of the equation
• B. Mean value of Y
• C. Correlation coefficient
• D. Slope of the regression line

Explanation: The coefficient of X is the slope, so the value 4 means that predicted Y increases by 4 units when X increases by one unit.

• A. 8
• B. 12
• C. 17
• D. 32

Explanation: Substituting X = 4 gives Y = 20 - 3(4) = 8. The negative slope indicates that the predicted value of Y decreases as X increases.

• A. r
• B. r squared
• C. 1 minus r
• D. The standard error

Explanation: The coefficient of determination is R squared, and in simple regression it equals the square of the correlation coefficient, r squared.

• A. -0.36
• B. -0.60
• C. 0.36
• D. 0.60

Explanation: The coefficient of determination is calculated as r squared, so (-0.6) squared equals 0.36.

• A. Uses one variable to predict another
• B. Always produces a value between -1 and 1
• C. Cannot show a negative relationship
• D. Requires both variables to have equal units

Explanation: Regression models the dependence of one variable on another and can be used for prediction.

• A. The variables have identical numerical values
• B. The variables tend to move in the same direction
• C. The variables have no measurable variation
• D. The variables always have a curved relationship

Explanation: Positive covariance means that observations above their respective means tend to occur together, as do observations below their means.

• A. Points lie on an upward-sloping straight line
• B. Points form a circular cloud around the mean
• C. Points lie on a downward-sloping straight line
• D. Points lie randomly along a horizontal band

Explanation: A downward-sloping straight line means that every increase in one variable is matched by a constant decrease in the other.

• A. The origin, (0, 0)
• B. The point of maximum observation
• C. The point of standard deviations
• D. The point of means, (X̄, Ȳ)

Explanation: Both regression equations pass through the means of the two variables, so their intersection is (X̄, Ȳ).

• A. 0.40
• B. 0.80
• C. 1.60
• D. 2.50

Explanation: The regression coefficient of Y on X is b_yx = r(s_y/s_x). Thus, b_yx = 0.8(10/5) = 1.6.

• A. Sum of absolute X values
• B. Sum of observed Y values
• C. Sum of squared residuals
• D. Product of the two means

Explanation: Least squares chooses the line for which the sum of the squared vertical residuals is as small as possible.

• A. Correlation and covariance
• B. Mean and standard deviation
• C. Slope and intercept
• D. Observed value and predicted value

Explanation: A residual is calculated as observed Y minus predicted Y for a particular observation.

• A. It uses the original numerical values
• B. It is based only on category labels
• C. It ignores the direction of association
• D. It always produces a positive value

Explanation: Pearson correlation uses deviations and products involving the actual numerical observations, so an outlier can substantially change its…

• A. Y on X
• B. X on Y
• C. X and Y jointly
• D. The means on the variances

Explanation: The phrase regression of X on Y means that X is the dependent or predicted variable and Y is the explanatory variable.

• A. 0.36
• B. 0.60
• C. 0.72
• D. 1.22

Explanation: The relationship is r² = b_yx × b_xy, so r² = 0.5 × 0.72 = 0.36. Since both regression coefficients are positive, r is positive, giving r…

• A. Become half its former value
• B. Double in value
• C. Remain exactly unchanged
• D. Change its sign

Explanation: The coefficient is b_yx = r(s_y/s_x). Doubling s_x while keeping r and s_y fixed divides the coefficient by two, without changing its sign.