Multiple Regression 1 FiniteQuest

Multiple Regression 1

Quantitative methods

1 / 10

In a multiple regression model with three independent variables, you have the following adjusted R-squared value: 0.85. If you add an additional independent variable, how would you expect the adjusted R-squared value to change if the new variable is not highly correlated with the existing ones?

Increase

Decrease

Remain unchanged

Cannot be determined

2 / 10

In a multiple regression analysis, the residual sum of squares (RSS) is 120 and the total sum of squares (TSS) is 200. What is the coefficient of determination (R-squared)?

0.4

0.6

0.8

1.0

3 / 10

You are performing a multiple regression analysis with three independent variables. The regression equation is:

Y = 2X1 – 3X2 + 4X3 – 6

If X1 is 5, X2 is 2, and X3 is 8, what is the predicted value of Y?

4 / 10

In a multiple regression analysis, you have a model with two independent variables, X1 and X2. The model is represented as:

Y = 3X1 + 2X2 + 5

If X1 is 4 and X2 is 7, what is the predicted value of Y?

5 / 10

The presence of heteroscedasticity in a multiple regression model can lead to what potential problem?

Inflated p-values for coefficients

Increased precision of coefficient estimates

Overfitting of the model

A lower coefficient of determination (R-squared)

6 / 10

Which of the following regression assumptions relates to the assumption that the residuals have a constant variance across all levels of the independent variables?

Linearity

Independence of errors

Homoscedasticity

Normality of residuals

7 / 10

What is multicollinearity in the context of multiple regression analysis?

It refers to the situation where the dependent variable is correlated with multiple independent variables.

It is the assumption that the residuals are normally distributed.

It occurs when two or more independent variables are highly correlated with each other.

It is a measure of the overall goodness-of-fit of the model.

8 / 10

In multiple regression, what is the assumption of independence of errors?

It assumes that the independent variables are uncorrelated with each other.

It assumes that the residuals (errors) are independent of each other.

It assumes that the residuals are normally distributed.

It assumes that the dependent variable is independent of the independent variables.

9 / 10

Which of the following is true regarding the coefficient of determination (R-squared) in multiple regression analysis?

It measures the strength of each independent variable’s relationship with the dependent variable.

It can have a maximum value of 1.0.

It is not influenced by the number of independent variables.

It is always equal to the correlation coefficient (r).

10 / 10

In the context of multiple regression analysis, what is the primary goal when modeling the relationship between multiple independent variables and a dependent variable?

Maximizing R-squared

Minimizing multicollinearity

Minimizing heteroscedasticity

Minimizing the number of independent variables

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