i. If an inverse relationship exists between the dependent variable and independent variables, the regression coefficients for the independent variables are positive. ii. Given a multiple linear equation Y' = 5.1 + 2.2X₁- 3.5X₂, assuming other things are held constant, an increase of one unit in the second independent variable will cause a -3.5 unit change in Y. iii. When the variance of the differences between the actual and the predicted values of the dependent variable are approximately the same, the variables are said to exhibit homoscedasticity. A) (i), (ii), and (iii) are all correct statements. B) (i) and (ii) are correct statements but not (iii). C) (i) and (iii) are correct statements but not (ii). D) (ii) and (iii) are correct statements but not (i). E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

- Statement (i) is incorrect because an inverse relationship between the dependent variable and an independent variable would result in a negative regression coefficient for that independent variable, not a positive one.- Statement (ii) is correct as it accurately describes the interpretation of regression coefficients in a multiple linear regression equation. A coefficient of -3.5 for an independent variable means that, holding other variables constant, a one-unit increase in this variable will result in a 3.5 unit decrease in the dependent variable Y.- Statement (iii) is also correct as it accurately describes homoscedasticity, which is a situation where the variances of the residuals (differences between actual and predicted values) are constant across all levels of the independent variables.

I If an Inverse Relationship Exists Between the Dependent Variable