(A) There can be more than two criterion
(B) There can be more than two predictors
(C) It indicates linear relation between one predicator and one criterion
(D) The equation for regression line contains partial regression coefficients
Choose the correct answer from the options given below :
Multiple Regression: Key Characteristics
Multiple regression is a statistical technique used to predict the value of a dependent variable (criterion) based on the values of two or more independent variables (predictors). Let's analyze the given statements:
Statement Analysis
- (A) There can be more than two criterion: This is generally false for standard multiple regression. Multiple regression typically involves one criterion variable and multiple predictor variables. If multiple criterion variables are involved, it's termed multivariate regression.
- (B) There can be more than two predictors: This is true. The defining feature of multiple regression is the use of multiple predictor variables to explain the variance in a single criterion variable.
- (C) It indicates linear relation between one predictor and one criterion: This statement describes simple linear regression, not multiple regression. Multiple regression examines the combined effect of multiple predictors on one criterion.
- (D) The equation for regression line contains partial regression coefficients: This is true. The multiple regression equation estimates the relationship between each predictor and the criterion, controlling for the influence of other predictors. These coefficients are known as partial regression coefficients (or standardized beta coefficients).
Conclusion on Statements
Based on the analysis, statements (B) and (D) accurately describe characteristics of multiple regression.
Final Answer Determination
The correct statements are (B) and (D). Therefore, the option indicating that only (B) and (D) are correct is the right choice.
Important Questions from Correlation and regression of two variables
In the case of two variables. the estimated regression equation is ŷ = 60 + 5x. The total sum of squares is 15730 and the sum of squares due to error is 1530. The estimated regression line based on this information is a ______.
For how many days were the number of road accident patients treated less than 4?
Number of Road Accident Patients Treated by a Hospital Emergency Ward
For 120 days, the number of road accident patients treated in the hospital's emergency ward is given below:
Number of patients / रोगियों की संख्या 0 1 2 3 4 5 6 7 Days / दिन 11 16 21 23 20 17 7 5 In a pie chart depicting total expenses of a company for the year 2016, raw material had a central angle of 45°. If total expenses were Rs 504 Lakhs, what were the company's expense on raw materials (in Rs lakhs)?
Find the mode from the following table.
Class and Frequency Table
The following data shows the class and frequency distribution:
Class / वर्ग 0-10 10-20 20-30 30-40 Frequency / आवृत्ति 15 25 30 20 Find P(A'/B'), given P(A) = 3/4, P(B) = 9/20 and P(A∩B) = 1/4?
