Which graphical device is used to get a first idea of correlation between two variables?
Correct answer B. Scatter diagram
Topic / 31 questions
Correlation and Regression MCQs
Correlation and Regression MCQs test the measurement of the strength and direction of a relationship between variables and the estimation of one variable from another. They help statistics students and PPSC, lecturer and UGC NET candidates. Each question gives an instant answer, so you can check key properties of r and the regression coefficients.
What does the regression coefficient byx represent?
Correct answer B. Average change in y for a unit change in x
In a least-squares regression line fitted with an intercept, what is the sum of the residuals?
Correct answer A. Zero
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Which pair of values cannot be the two regression coefficients of the same data?
Correct answer B. byx = 1.5, bxy = 0.8
The method of least squares chooses the regression line of y on x so as to minimise what?
Correct answer B. Sum of squared vertical deviations of points from the line
The two regression lines are x + 2y = 10 and 2x + y = 11. What is the mean of x?
Correct answer C. 4
If r(x, y) = 0.4, u = 2x + 3 and v = −3y + 1, what is r(u, v)?
Correct answer A. −0.4
If every pair of observations satisfies y = 5 − 2x exactly, what is the correlation coefficient?
Correct answer D. −1
Pearson’s correlation coefficient measures the strength of which kind of relationship?
Correct answer B. Linear relationship
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For 5 pairs of ranks, the sum of squared rank differences Σd² is 8. What is Spearman’s rank correlation coefficient?
Correct answer B. 0.6
The term ‘regression’ was first used in statistics by which scientist?
Correct answer A. Sir Francis Galton
If Cov(x, y) = 12, σx = 4 and σy = 5, what is the correlation coefficient?
Correct answer D. 0.6
Using the regression equation y = 3 + 2x, what is the estimated value of y when x = 10?
Correct answer C. 23
Given r = 0.5, σx = 4 and σy = 8, what is the regression coefficient of y on x?
Correct answer D. 1.0
For x: 1, 2, 3, 4, 5 and y: 2, 4, 5, 4, 5, what is the least-squares regression line of y on x?
Correct answer A. y = 2.2 + 0.6x
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For the data x: 1, 2, 3, 4, 5 and y: 2, 4, 5, 4, 5, what is Pearson’s correlation coefficient (to two decimals)?
Correct answer C. 0.77
When r = 0, how are the two regression lines placed relative to each other?
Correct answer A. Perpendicular to each other
When the correlation between x and y is perfect (r = ±1), the two regression lines are related how?
Correct answer C. They coincide
At which point do the two lines of regression intersect?
Correct answer C. (x̄, ȳ)
If the two regression coefficients are byx = −0.9 and bxy = −0.4, what is r?
Correct answer C. −0.6
About Correlation and Regression MCQs
This Statistics topic tests short properties that are easy to state and easy to confuse. Questions ask for the range of the correlation coefficient and of the partial correlation coefficient, both from minus one to plus one, what happens to regression coefficients when r is zero, why the regression coefficients and r always have the same sign, and what follows if one regression coefficient is greater than one. You will also be asked what kind of technique regression analysis is. Learning these rules as a short list is an efficient way to secure marks in statistics papers.
Exams that include Correlation and Regression MCQs
Pakistan
- PPSC
- FPSC
- Lecturer tests
- NTS
India
- UGC NET
- State PSC exams
Bangladesh
- BCS
- University admission tests (DU, RU, JU)
Frequently asked questions
What is the range of the correlation coefficient?
The correlation coefficient r always lies between minus one and plus one. A value of plus one shows perfect positive correlation, minus one shows perfect negative correlation, and zero shows no linear relationship. The partial correlation coefficient has the same range.
What happens to regression coefficients when r is zero?
When r is zero, both regression coefficients are zero, because each coefficient equals r multiplied by a ratio of standard deviations. The two regression lines are then parallel to the axes and perpendicular to each other, showing no linear relationship.
Last reviewed October 2026