All Free Quantitative Methods MCQs with Answers

• 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.

• A. Spearman's rank correlation
• B. Pearson's product-moment correlation
• C. The coefficient of variation
• D. The standard error of the mean

Explanation: Spearman's rank correlation measures association using the relative order of observations.

• A. Be multiplied by 10
• B. Remain unchanged
• C. Be divided by 10
• D. Become equal to zero

Explanation: Positive changes of measurement scale do not alter the direction or strength of linear association.

• A. A perfect positive linear relationship
• B. No variation in either variable
• C. A strong curved relationship
• D. Exactly equal means

Explanation: Pearson's correlation measures linear association, so a strong nonlinear pattern may produce a value near zero.

• A. The dependent variable has zero variance
• B. The independent variable has zero variance
• C. The correlation must equal exactly one
• D. The independent variable has nonzero variance

Explanation: The slope uses the variation in the independent variable in its denominator.

• A. The predicted value of Y when X equals zero
• B. The change in Y for one unit of X
• C. The average error in predicting Y
• D. The correlation between X and Y

Explanation: The intercept is the fitted value of Y at X equal to zero. The slope, not the intercept, describes the expected change in Y for a one-unit…

• A. Income rises by 2.5 rupees per year
• B. Experience rises by 2.5 years per rupee
• C. Predicted income rises by 2.5 units per extra year
• D. Income and experience have correlation 2.5

Explanation: The slope gives the change in the predicted response for one unit of the explanatory variable.

• A. Its numerical value is always unit-free
• B. It must lie between zero and one
• C. Its units are units of X divided by units of Y
• D. Its units are units of Y divided by units of X

Explanation: A regression slope is a rate of change, so its units are response units per explanatory-variable unit.

• A. 6.4 percent
• B. 36 percent
• C. 64 percent
• D. 80 percent

Explanation: The coefficient of determination is the proportion of response variation explained by the regression model.

• A. Always equal to one
• B. Always equal to zero when an intercept is included
• C. Always equal to the correlation coefficient
• D. Always equal to the regression slope

Explanation: When the fitted regression includes an intercept, the residuals balance so their algebraic sum is zero.

• A. This is possible in ordinary least-squares regression
• B. It proves that Y has zero variance
• C. This is impossible when both standard deviations are positive
• D. It means the intercept must be negative

Explanation: The slope for predicting Y from X equals the correlation multiplied by the ratio of the standard deviations.