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AIM 4: Explain the concept of multicollinearity and implications it has on modeling.

1、Which of the following statements regarding multicollinearity is FALSE?

A) Multicollinearity may be a problem even if the Multicollinearity is not perfect.

B) Multicollinearity makes it difficult to determine the contribution to explanation of the dependent variable of an individual explanatory variable.

C) Multicollinearity may be present in any regression model.

D) If the t-statistics for the individual independent variables are insignificant, yet he F-statistic is significant, this indicates the presence of Multicollinearity.

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The correct answer is C

Multicollinearity is not an issue in simple regression.

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2、A variable is regressed against three other variables, x, y, and z. Which of the following would NOT be an indication of multicollinearity? X is closely related to:

A) 3y + 2z.

B) 3.

C) y2.

D) 9y, and x is closely related to 4z.

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The correct answer is C

If x is related to y2, the relationship between x and y is not linear, so multicollinearity does not exist. If x is equal to a constant (3), it will be correlated with the intercept term.

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3、An analyst runs a regression of portfolio returns on three independent variables.  These independent variables are price-to-sales (P/S), price-to-cash flow (P/CF), and price-to-book (P/B).  The analyst discovers that the p-values for each independent variable are relatively high.  However, the F-test has a very small p-value.  The analyst is puzzled and tries to figure out how the F-test can be statistically significant when the individual independent variables are not significant.  What violation of regression analysis has occurred?

A) serial correlation.

B) conditional heteroskedasticity.

C) multicollinearity.

D) unconditional heteroskedasticity.

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AIM 3: List the assumptions of the multiple linear regression model.

1、Which of the following statements least accurately describes one of the fundamental multiple regression assumptions?

A) The error term is normally distributed.

B) The variance of the error terms is not constant (i.e., the errors are heteroskedastic).

C) The independent variables are not random.

D) There is no exact linear relationship between any two or more independent variables.

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The correct answer is B

The variance of the error term IS assumed to be constant, resulting in errors that are homoskedastic.

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2、One of the underlying assumptions of a multiple regression is that the variance of the residuals is constant for various levels of the independent variables. This quality is referred to as:

A) a normal distribution.

B) homoskedasticity.

C) a linear relationship.

D) serial correlation.

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The correct answer is B

Homoskedasticity refers to the basic assumption of a multiple regression model that the variance of the error terms is constant.

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The correct answer is A

The slope coefficient is the change in the dependent variable for a one-unit change in the independent variable.