Exam 15: Model Building and Model Diagnostics

As we increase the number of independent variables in a multiple regression model,the F statistic in the analysis of variance table for the multiple regression model will ________ increase.

If successive values of the residuals are close together,then there is a(n)___________ autocorrelation,and the value of the Durbin-Watson statistic is _________.

In the quadratic regression model ,the v₂ term represents the:

Significant _________ may exist when the overall F-statistic is significant and the individual t statistics for all independent variables is insignificant.

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of adjusted R² will ____________ decrease.

In a multiple regression analysis,the current model has three independent variables.The analyst decides to add another (fourth)independent variable while retaining the other three independent variables.As a result of this addition,the value of SSE will ____________ decrease.

Inclusion of redundant independent variables in the regression model increases the problem of __________.

If the multiple coefficient of determination that relates x₂ to all the other independent variables,R²(x₂)= .94,calculate the variance inflation factor for x₂.Should the analyst be concerned about multicollinearity? Why?

In regression analysis the _________ is used to identify outliers with respect to their x values and ________ is used to identify outliers with respect to their y values.

Below is a partial multiple regression computer output based on a quadratic regression model. Test the overall usefulness of the model at $\alpha$ = .05.Calculate the F statistic and make your decision.

Given the regression model y = $\beta$ ₀ + $\beta$ ₁X₁ + $\beta$ ₂X₂ + $\beta$ ₃X₁² + $\beta$ ₄X₂² + $\varepsilon$ ,if we wish to test the significance of higher order terms, (X₁² and X₂²)we would use the following test.

In a multiple regression model with 4 independent variables and 25 observations,an observation's actual y value is 128.2,and the predicted value of the dependent variable based on the multiple regression equation is equal to 114.7.The computer output also shows that MSE is equal to 144 and the leverage value is 0.19.Calculate the Cook's D statistic for this observation.Based on the Cook's statistic value is this observation influential? Why?

___________ is an iterative variable selection procedure that allows an independent variable to be added to a multiple regression model in one iteration and deleted during the next iteration?

Cook's distance measure is used in:

Cook's distance is a way to determine whether an observation is influential.

In a regression model a(n)______ is an observation that is well separated from the rest of the data with respect to its y value and/or its x values.

Multicollinearity hinders the regression model's ability to predict the dependent variable on the basis of a combination of values of the independent variable in the experimental region.

When the quadratic regression model y = $\beta$ ₀ + $\beta$ ₁x + $\beta$ ₂x² + $\varepsilon$ is used,the term _____ shows the rate of curvature of the parabola.

When using a multiple linear regression model,data transformations on the dependent variable may be used in order to correct a violation of a(n)__________ of the multiple linear regression model.

In multiple regression analysis,if the simple correlation coefficient between the dependent variable and one of the independent variables is .95,then this indicates that the problem of multicollinearity exists.