All Free Statistics MCQs with Answers
Every Statistics question in the bank, across all chapters, each with the correct answer and a written explanation. Free and unlimited, with no account needed.
545 questions · page 2 of 55
11. If bxy = -.8 by x = 1.2 then value of r is ________________?
- A. √.96
- B. √-.96
- C. 0
- D. None of these
Explanation: The product of the two regression coefficients equals r², so here r² = (−0.8)(1.2) = −0.96. A squared real correlation cannot be negative, making all numerical options invalid.
Correct answer: None of these12. Correlation coefficient is ___________ with respect to x and y?
- A. +vely
- B. Non-normal
- C. Symmetrical
- D. Skewed
Explanation: Correlation is symmetric because interchanging x and y does not change its value, so rxy = ryx. It is therefore neither skewed nor directional with respect to the two variables.
Correct answer: Symmetrical13. Correlation coefficient is _________ of origin and unit of measurement?
- A. Origin
- B. Dependence
- C. Independence
- D. None
Explanation: The correlation coefficient is unaffected by changes of origin and unit of measurement, although changing units can alter the regression coefficients. This makes it a scale-free measure of linear association.
Correct answer: Independence14. Correlation is _____________ of regression coefficients?
- A. A.M.
- B. G.M.
- C. M.D.
- D. H.M.
Explanation: The correlation coefficient satisfies r² = bxy × byx, so its magnitude is the geometric mean of the two regression coefficients, with the common sign determined separately. Hence correlation is described as their geometric mean.
Correct answer: G.M.15. In correlation, both variables are______________?
- A. Random
- B. Fixed
- C. Non-random
- D. Experimental
Explanation: In correlation analysis, x and y are treated symmetrically as random variables, and their joint variation is studied. In simple regression, one variable is commonly treated as the dependent variable, which distinguishes the two methods.
Correct answer: Random16. If y = 2 + 6x then value of y intercept is _________________?
- A. 6
- B. 2
- C. 0
- D. None
Explanation: Writing the equation as y = a + bx, the y-intercept is the constant term a, which is 2. The value 6 is the slope, showing the change in y for a one-unit change in x.
Correct answer: 217. A model is linear if it is linear in the dependent variable and also in ______________?
- A. Parameter
- B. Independent variable
- C. Error term
- D. Non of these
Explanation: A linear model must be linear in its parameters, even if the independent variable appears in a transformed form such as x² or log x. Thus, linearity in the parameter is the defining requirement.
Correct answer: Parameter18. The two regression co-efficient always have the __________ sign?
- A. Different
- B. Same
- C. None of these
- D. +ve
Explanation: The two regression coefficients satisfy bxy × byx = r², which is non-negative, so they must have the same sign, or both be zero. They cannot have opposite signs.
Correct answer: Same19. If r, between u = x and y = -x is _______________?
- A. +1
- B. -1
- C. 0
- D. Non of these
Explanation: The relation y = -x is a perfect downward straight line, so as x increases, y decreases exactly proportionally. Therefore, the correlation coefficient is -1.
Correct answer: -120. Correlation coefficient lies between__________________?
- A. 0 ≤ r ≤ 1
- B. 0 ≤ r ≤ -1
- C. -1 ≤ r ≤ 1
- D. 1 ≤ r ≤ 0
Explanation: Correlation measures the strength and direction of linear association, with -1 representing perfect negative association and +1 perfect positive association. Hence its range is -1 ≤ r ≤ 1.
Correct answer: -1 ≤ r ≤ 1