Exam 17: Multiple Regression

The total variation in y is equal to SSR + ____________________.

The Durbin-Watson test allows the statistics practitioner to determine whether there is evidence of first-order autocorrelation.

A multiple regression model has:

In reference to the equation ,the value 0.60 is the average change in y per unit change in x₂,regardless of the value of x₁.

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} What is the value of the calculated F-test statistic that is missing from the output for testing whether the whole regression model is significant?

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 coefficient of determination? What does this statistic tell you?

The range of the values of the Durbin-Watson statistic,d,is 0 ≤d≤ 4.

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} What are the numerator and denominator degrees of freedom for the F-statistic?

In multiple regression analysis,the ratio MSR/MSE yields the:

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} Interpret the coefficient b₃.

Multicollinearity is a situation in which two or more of the independent variables are highly correlated with each other.

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

The coefficient of determination R² measures the proportion of variation in y that is explained by the explanatory variables included in the model.

If the value of the Durbin-Watson statistic,d,satisfies the inequality d_L≤d≤d_U,where d_L and d_U are the critical values for d,then the test for positive first-order autocorrelation is inconclusive.

An adverse effect of multicollinearity is that the estimated regression coefficients of the independent variables that are correlated tend to have large sampling ____________________.

The range of the values of the Durbin-Watson statistic d is ____________________.

When an additional explanatory variable is introduced into a multiple regression model,coefficient of determination adjusted for degrees of freedom can never decrease.

Life Expectancy An actuary wanted to develop a model to predict how long individuals will live.After consulting a number of physicians,she collected the age at death (y),the average number of hours of exercise per week (x₁),the cholesterol level (x₂),and the number of points that the individual's blood pressure exceeded the recommended value (x₃).A random sample of 40 individuals was selected.The computer output of the multiple regression model is shown below. THE REGRESSION EQUATION IS y = 55.8 + 1.79x₁− 0.021x₂− 0.061x₃ ​ S = 9.47 ​ R−Sq = 22.5% ANALYSIS OF VARIANCE ​ ​ -{Life Expectancy Narrative} Interpret the coefficient b₂.

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} Does this data provide enough evidence at the 1% significance level to conclude that the final grade and the midterm exam score are positively linearly related?

When an additional explanatory variable is introduced into a multiple regression model,the coefficient of determination will never decrease.