Exam 15: Multiple Regression Model Building

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker ( ), the number of years of education received ( ), the number of years at the previous job ( ), a dummy variable for marital status ( 1 = married, 0 = otherwise), a dummy variable for head of household ( 1 = yes, 0 = no)and a dummy variable for management position ( 1 = yes, 0 = no). The coefficient of multiple determination ( )for the regression model using each of the 6 variables as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993. The partial results from best-subset regression are given below: -Referring to Scenario 15-6, what is the value of the Mallow's statistic for the model that includes and

The logarithm transformation can be used

SCENARIO 15-5 What are the factors that determine the acceleration time (in sec.)from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu.ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The coefficient of multiple determination ( )for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Scenario 15-5, what is the value of the variance inflationary factor of Cargo Vol?

SCENARIO 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Let Y = % Passing as the dependent variable, Attendance, Salaries and Spending. The coefficient of multiple determination ( )of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743. The output from the best-subset regressions is given below: Following is the residual plot for % Attendance: Following is the output of several multiple regression models: -Referring to Scenario 15-4, which of the following models should be taken into consideration using the Mallows' statistic?

SCENARIO 15-1 A certain type of rare gem serves as a status symbol for many of its owners.In theory, for low prices, the demand increases, and it decreases as the price of the gem increases.However, experts hypothesize that when the gem is valued at very high prices, the demand increases with price due to the status owners believe they gain in obtaining the gem.Thus, the model proposed to best explain the demand for the gem by its price is the quadratic model: where Y = demand (in thousands)and X = retail price per carat. This model was fit to data collected for a sample of 12 rare gems of this type.A portion of the computer analysis obtained from Microsoft Excel is shown below: SUMMARY OUTPUT -Referring to Scenario 15-1, what is the value of the test statistic for testing whether there is an upward curvature in the response curve relating the demand (Y)and the price (X)?

The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.

SCENARIO 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing), daily mean of the percentage of students attending class (% Attendance), mean teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Let Y = % Passing as the dependent variable, Attendance, Salaries and Spending. The coefficient of multiple determination ( )of each of the 3 predictors with all the other remaining predictors are, respectively, 0.0338, 0.4669, and 0.4743. The output from the best-subset regressions is given below: Following is the residual plot for % Attendance: Following is the output of several multiple regression models: -Referring to Scenario 15-4, the "best" model using a 5% level of significance among those chosen by the statistic is

SCENARIO 15-3 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a curvilinear model to this data.The results obtained by Microsoft Excel follow SUMMARY OUTPUT -Referring to Scenario 15-3, suppose the chemist decides to use a t test to determine if there is a significant difference between a linear model and a curvilinear model that includes a linear term.If she used a level of significance of 0.05, she would decide that the linear model is sufficient.

The statistic is used

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker ( ), the number of years of education received ( ), the number of years at the previous job ( ), a dummy variable for marital status ( 1 = married, 0 = otherwise), a dummy variable for head of household ( 1 = yes, 0 = no)and a dummy variable for management position ( 1 = yes, 0 = no). The coefficient of multiple determination ( )for the regression model using each of the 6 variables as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993. The partial results from best-subset regression are given below: -Referring to Scenario 15-6, what is the value of the variance inflationary factor of Age?

SCENARIO 15-5 What are the factors that determine the acceleration time (in sec.)from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu.ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The coefficient of multiple determination ( )for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Scenario 15-5, what is the value of the variance inflationary factor of SUV?

SCENARIO 15-3 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a curvilinear model to this data.The results obtained by Microsoft Excel follow SUMMARY OUTPUT -Referring to Scenario 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant.Using a level of significance of 0.05, she would decide that the linear term is significant.

SCENARIO 15-5 What are the factors that determine the acceleration time (in sec.)from 0 to 60 miles per hour of a car? Data on the following variables for 171 different vehicle models were collected: Accel Time: Acceleration time in sec. Cargo Vol: Cargo volume in cu.ft. HP: Horsepower MPG: Miles per gallon SUV: 1 if the vehicle model is an SUV with Coupe as the base when SUV and Sedan are both 0 Sedan: 1 if the vehicle model is a sedan with Coupe as the base when SUV and Sedan are both 0 The coefficient of multiple determination ( )for the regression model using each of the 5 variables as the dependent variable and all other X variables as independent variables are, respectively, 0.7461, 0.5676, 0.6764, 0.8582, 0.6632. -Referring to Scenario 15-5, there is reason to suspect collinearity between some pairs of predictors based on the values of the variance inflationary factor.

SCENARIO 15-3 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a curvilinear model to this data.The results obtained by Microsoft Excel follow SUMMARY OUTPUT -Referring to Scenario 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant.The value of the test statistic is ______.

SCENARIO 15-3 A chemist employed by a pharmaceutical firm has developed a muscle relaxant.She took a sample of 14 people suffering from extreme muscle constriction.She gave each a vial containing a dose (X)of the drug and recorded the time to relief (Y)measured in seconds for each.She fit a curvilinear model to this data.The results obtained by Microsoft Excel follow SUMMARY OUTPUT -Referring to Scenario 15-3, suppose the chemist decides to use a t test to determine if the linear term is significant.The p-value of the test is ______.

Using the best-subsets approach to model building, models are being considered when their

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker ( ), the number of years of education received ( ), the number of years at the previous job ( ), a dummy variable for marital status ( 1 = married, 0 = otherwise), a dummy variable for head of household ( 1 = yes, 0 = no)and a dummy variable for management position ( 1 = yes, 0 = no). The coefficient of multiple determination ( )for the regression model using each of the 6 variables as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993. The partial results from best-subset regression are given below: -Referring to Scenario 15-6, the model that includes should be among the appropriate models using the Mallow's statistic.

SCENARIO 15-6 Given below are results from the regression analysis on 40 observations where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Y)and the independent variables are the age of the worker ( ), the number of years of education received ( ), the number of years at the previous job ( ), a dummy variable for marital status ( 1 = married, 0 = otherwise), a dummy variable for head of household ( 1 = yes, 0 = no)and a dummy variable for management position ( 1 = yes, 0 = no). The coefficient of multiple determination ( )for the regression model using each of the 6 variables as the dependent variable and all other X variables as independent variables are, respectively, 0.2628, 0.1240, 0.2404, 0.3510, 0.3342 and 0.0993. The partial results from best-subset regression are given below: -Referring to Scenario 15-6, the model that includes and should be among the appropriate models using the Mallow's statistic.

An independent variable is considered highly correlated with the other independent variables if

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