All Free Statistics MCQs with Answers

• A. 0
• B. 1
• C. 2
• D. Infinity

Explanation: The regression coefficients satisfy b_yx = r(s_y/s_x) and b_xy = r(s_x/s_y).

• A. Absolute measure
• B. Relative measure
• C. Both a and b
• D. None of the above

Explanation: A correlation coefficient is a relative, unit-free measure of the strength and direction of association.

• A. Absolute measure
• B. Relative measure
• C. Both a and b
• D. None of these

Explanation: Regression coefficients carry units, such as units of the dependent variable per unit of the predictor, so regression is treated as an…

• A. Greater than 1
• B. Less than 1
• C. Remain same
• D. No effect

Explanation: The two regression coefficients satisfy Bxy × Byx = r², and r² cannot exceed 1.

• A. Same
• B. Change
• C. Differ
• D. None of these

Explanation: Both regression coefficients have the same sign as the correlation coefficient because their signs are determined by r.

• A. 0to1
• B. -1to1
• C. 0to-1
• D. 0 to infinity

Explanation: A partial correlation coefficient measures the direction and strength of a linear relationship after controlling for other variables.

• A. Neyman person
• B. R A Fisher
• C. Sir F Galton
• D. Karl Pearson

Explanation: Sir Francis Galton introduced the term regression while studying the tendency of extreme parent and offspring measurements to move toward…

• A. Regressand
• B. Predicted
• C. Response
• D. All of above

Explanation: The dependent variable is the response or predicted variable, and in regression terminology it is also called the regressand.

• A. Fixed
• B. Random variable
• C. Whole
• D. None of above

Explanation: A response variable is the outcome being measured or predicted, so its observed value is treated as a random variable.

• A. -1
• B. +1
• C. .6
• D. 0

Explanation: Independence implies zero covariance, and therefore the correlation coefficient is zero when the variances are defined and nonzero.

• 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. +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.

• 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…

• 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…

• 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.

• 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.

• 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.

• 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.

• 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.

• 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…