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 1 of 55
1. When r is zero than both regression coefficients are________?
- 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). Therefore, when r is zero and the standard deviations are nonzero, both regression coefficients are zero.
Correct answer: 02. Correlation coefficient is__________?
- 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. Its value remains unchanged if the measurement units are changed, unlike an absolute measure.
Correct answer: Relative measure3. Regression analysis is an_______?
- 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 absolute measure in this classification. Correlation, by contrast, is unit-free and relative.
Correct answer: Absolute measure4. If (Bxy>1)then (Byx)?
- 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. Therefore, if Bxy is greater than 1, Byx must be less than 1.
Correct answer: Less than 15. In regression the sign of (B's) and (r)?
- 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. Thus positive r gives positive regression coefficients, and negative r gives negative ones.
Correct answer: Same6. The range of partial correlation coefficient?
- 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. Like ordinary correlation, it ranges from -1 to +1.
Correct answer: -1to17. The word regression was first founded by_________?
- 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 the average. Karl Pearson later developed important mathematical tools for regression and correlation.
Correct answer: Sir F Galton8. The dependent variable also called_________?
- 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. Thus all three descriptions refer to the dependent variable.
Correct answer: All of above9. Response variable is a_________?
- 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. The explanatory variable is used to explain or predict changes in the response.
Correct answer: Random variable10. If x and y are Independent to each other the coefficient of correlation is _____________?
- 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. Values such as +1 or -1 indicate perfect linear relationships, not independence.
Correct answer: 0