Question 1

Only when all three of the hat matrix elements hi, the Studentized deleted residuals ti and the Cook's distance statistic Di reveal consistent result should an observation be removed from the regression analysis.

Accepted Answer

This statement is true. It is important to consider all three of these statistics together when deciding whether or not to remove an observation from a regression analysis. If all three statistics consistently indicate that an observation should be removed, then it is likely that the observation is an outlier that is unduly influencing the regression results.

Question 2

Using the Studentized residuals ti to determine influential points in a multiple regression model with k independent variable and n observations and letting tn-k-2 denote the upper critical value of a two-tail t test with a 0.10 level of significance, Xi is an influential point if a) $| t | < t _ { n - k - 1 }$ b) $| t | > t _ { n - k - 1 }$ c) $\left| t _ { i } \right| < t _ { n - k - 2 }$ d) $\left| t _ { i } \right| > t _ { n - k - 2 }$

Accepted Answer

The answer of Using the Studentized residuals ti to determine...

Question 3

The following two statements are equivalent in meaning:A.The test of significance for a specific regression coefficient in a multiple regression model is a test of significance for adding that variable into the model given the other variable is included.B.The t test for a regression coefficient is actually a test for the contribution of that independent variable.

Accepted Answer

Both statements essentially say that the test of significance for a regression coefficient in a multiple regression model is a test of the contribution (or importance) of that independent variable to the model, given the other variables are already included. Therefore, both statements are equivalent in meaning.

Question 4

To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term.

Accepted Answer

Interaction terms are used to examine if the effect of one independent variable on the dependent variable changes at different levels of another independent variable. To properly examine the effect of a categorical independent variable in a multiple linear regression model, we typically use dummy coding (or one-hot encoding) to convert the categorical variable into numerical form, not necessarily an interaction term.

Question 5

Which of the following is NOT used to determine observations that have influential effect on the fitted model?
A)The hat matrix elements hi
B)The studentized deleted residuals ti
C)The Cp statistic
D)Cook's distance statistic

Accepted Answer

The Cp statistic is a measure of model fit, but it is not used specifically to identify influential observations. The hat matrix elements (hi), studentized deleted residuals (ti), and Cook's distance statistic are all commonly used for identifying influential observations.

Question 6

A plot of the residuals versus an independent X shows evidence of a curvilinear effect.Which of the following statements is a possible solution?
A)Transform the Y variable.
B)Use the Durbin-Watson statistic to determine if there is autocorrelation.
C)Add a curvilinear independent variable to the multiple regression model.
D)Check for autocorrelation among the residuals.

Accepted Answer

A curvilinear effect suggests that the relationship between the dependent and independent variables is not linear, thus adding a curvilinear independent variable to the model can address this issue. Transforming the Y variable may not solve the issue of a curvilinear effect. Using the Durbin-Watson statistic is relevant to detecting autocorrelation, not curvilinearity. Checking for autocorrelation among the residuals is also not relevant to addressing the issue of a curvilinear effect.

Question 7

Using the hat matrix elements hi to determine influential points in a multiple regression model with k independent variable and n observations, Xi is an influential point if a) $h _ { i } < 2 ( k + 1 ) / n$ b) $h _ { i } > 2 ( k + 1 ) / n$ c) $h _ { i } < n ( k + 1 ) / 2$ d) $h _ { i } > n ( k + 1 ) / 2$

Accepted Answer

The answer of Using the hat matrix elements hi to...

Quiz 13: Multiple Regression

Only when all three of the hat matrix elements hi, the Studentized deleted residuals ti and the Cook's distance statistic Di reveal consistent result should an observation be removed from the regression analysis.

To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term.

Which of the following is NOT used to determine observations that have influential effect on the fitted model?

A plot of the residuals versus an independent X shows evidence of a curvilinear effect.Which of the following statements is a possible solution?