Exam 17: Multiple Regression

For a multiple regression model the following statistics are given: Total variation in y = 250,SSE = 50,k = 4,and n = 20.Then,the coefficient of determination adjusted for the degrees of freedom is:

To use the Durbin-Watson test to test for negative first-order autocorrelation,the null hypothesis will be H₀: ____________________ (there is/there is no)first-order autocorrelation.

In a multiple regression analysis,if the model provides a poor fit,this indicates that:

A high value of the coefficient of determination significantly above 0 in multiple regression,accompanied by insignificant t-statistics on all parameter estimates,very often indicates a high correlation between independent variables in the model.

In testing the significance of a multiple regression model with three independent variables,the null hypothesis is . ​ ​

A multiple regression model has the form .The coefficient b₁ is interpreted as the average change in y per unit change in x₁.

There are several clues to the presence of multicollinearity.One clue is when an independent variable is added or deleted,the regression coefficients for the other variables ____________________.

Consider the following statistics of a multiple regression model: n = 25,k = 5,b₁ = −6.31,and sε = 2.98.Can we conclude at the 1% significance level that x₁ and y are linearly related?

Real Estate Builder A real estate builder wishes to determine how house size is influenced by family income,family size,and education of the head of household.House size is measured in hundreds of square feet,income is measured in thousands of dollars,and education is measured in years.A partial computer output is shown below. SUMMARY OUTPUT Regression Statistics Multiple R 0.865 R Square 0.748 Adjusted R Square 0.726 Standard Error 5.195 Observations 50 ANOVA ​ ​ -{Real Estate Builder Narrative} Suppose the builder wants to test whether the coefficient on education is significantly different from 0.What is the value of the relevant t-statistic?

There are several clues to the presence of multicollinearity.One clue is when a regression coefficient exhibits the wrong ____________________.

Small values of the Durbin-Watson statistic d (d < 2)indicate a negative first-order autocorrelation.

In regression analysis,the total variation in the dependent variable y,measured by ,can be decomposed into two parts: the explained variation,measured by SSR,and the unexplained variation,measured by SSE.

In a multiple regression model,the error variable ε is assumed to have a mean of:

If multicollinearity exists among the independent variables included in a multiple regression model,then:

Student's Final Grade A statistics professor investigated some of the factors that affect an individual student's final grade in her course.She proposed the multiple regression model ,where y is the final grade (out of 100 points),x₁ is the number of lectures skipped,x₂ is the number of late assignments,and x₃ is the midterm exam score (out of 100).The professor recorded the data for 50 randomly selected students.The computer output is shown below. THE REGRESSION EQUATION IS ​ ​ ​ S = 13.74 R−Sq = 30.0% ​ ANALYSIS OF VARIANCE ​ ​ -{Student's Final Grade Narrative} What is the adjusted coefficient of determination? What does this statistic tell you?

A multiple regression equation includes 5 independent variables,and the coefficient of determination is 0.81.The percentage of the variation in y that is explained by the regression equation is:

In reference to the equation ,the value −0.80 is the y-intercept.

Multicollinearity will result in excessively low standard errors of the parameter estimates reported in the regression output.

A multiple regression model has the form .As x₃ increases by one unit,with x₁ and x₂ held constant,the y on average is expected to:

Some of the requirements for the error variable in a multiple regression model are that the standard deviation is a(n)____________________ and the errors are ____________________.