Exam 12: Multiple Regression and Model Building

The normal plot is a residual plot that checks the assumption that,for any point in the experimental region,the population of potential error terms is normally distributed.

Which one of the following is not an assumption about the error term in a regression model?

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.

Consider a multiple regression analysis with 20 observations on each of three independent variables and the dependent variable.When performing an overall F test for the model,the critical F value would have ______ numerator degrees of freedom and _______ denominator degrees of freedom.

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 X1 -0.007207 0.0031 X2 0.0011336 0.00122 X3 0.9324 0.373 Analysis of Variance SS Source df 31.308 Regression 3 9.378 -Calculate R².

Below is a partial multiple regression ANOVA table. Source SS df Model 0.242 2 Error 0.105 3 -What is the value of F?

A multiple linear regression analysis involving 45 observations resulted in the following least squares prediction equation: $\hat { y } = .408 + 1.3387 x _ { 1 } + 2.1 x _ { 2 }$ . The SSE for the above model is 49. Addition of two other independent variables to the model,resulted in the following multiple linear regression equation: $\hat { y } = 1.2 + 3 x _ { 1 } + 12 x _ { 2 } + 4 x _ { 3 } + 8 x _ { 4 }$ . The latter model's SSE is 40. -Determine the degrees of freedom regression (explained variation),degrees of freedom error (unexplained variation),and total degrees of freedom for the latter model (the model with four independent variables).

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Dev Constant 99.3883 1 -0.007207 0.0031 2 0.0011336 0.00122 3 0.9324 0.373 Analysis of Variance Source df SS Regression 3 31.308 Error (residual) 16 9.378 -How many observations were taken?

All of the following are desirable outcomes for a multiple regression model except:

Use the following correlation matrix and determine the best multiple regression prediction equation that has no significant multicollinearity.

Consider the following partial computer output for a multiple regression model. Predictor Coefficient Standard Deviation Constant 41.225 6.380 1.081 1.353 -18.404 4.547 Analysis of Variance Source Regression 2 2270.11 Error (residual) 26 3585.75 -What is the total sum of squares (total variation)?

Below is a partial multiple regression ANOVA table. Source SS df Model 0.242 2 Error 0.105 3 -What is the mean square error?

Which is not an assumption of a multiple regression model?

Test the usefulness of variable x5 in the model at alpha = .05.Calculate the t statistic and state your conclusions.

In a multiple regression model,the residuals were plotted against the values of one of the independent variables.The plot exhibited a funnelling out pattern of residuals.This means that as the value of the independent variable increases,the spread of the error terms tends to ________ and the model assumption of ________ is violated.

The multiple coefficient of _____ measures the proportion of the variation in y (response variable)explained by the multiple regression model or the set of independent variables included in the multiple regression equation.

In a multiple regression,the least squares point estimates are values which maximize the sums of squared error.

In multiple regression analysis,a desirable residual plot has what type of appearance?

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

A researcher in human resources has expressed concern about the differences in job satisfaction results across units within an organization. The researcher conducts a study to investigate what factors could account for the differences. The researcher looked at a random sample of units across the organization and used the factors of percentage of employees with a university degree, the average age of the employees, and the average salary of employees within a unit. The results of the study are presented below: Predictor Coef SE Coef Constant 35.178 7.595 Degree 0.22073 0.07131 Age 0.3353 0.1901 Salary 0.0930 0.1675 $s = 7.62090$ Analysis of Variance Source DF SS Regression 3 1053.09 Residual Error 32 1858.50 Source DF Seq SS Degree 1 672.10 Age 1 363.09 Salary 1 17.90 -Using the results above,the value of R² is _____.