Exam 14: Introduction to Multiple Regression

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions)is influenced by gross domestic product ($ billions)and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. -Referring to Table 14-3,the p-value for the aggregated price index is

TABLE 14-17 Given below are results from the regression analysis where the dependent variable is the number of weeks a worker is unemployed due to a layoff (Unemploy)and the independent variables are the age of the worker (Age)and a dummy variable for management position (Manager: 1 = yes,0 = no). The results of the regression analysis are given below: -True or False: Referring to Table 14-17,the null hypothesis should be rejected at a 10% level of significance when testing whether age has any effect on the number of weeks a worker is unemployed due to a layoff while holding constant the effect of the other independent variable.

TABLE 14-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y).To provide its customers with information on that matter,a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁)and the amount of insulation in inches (X₂).Given below is EXCEL output of the regression model. Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672 -Referring to Table 14-6,what can we say about the regression model?

TABLE 14-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y).To provide its customers with information on that matter,a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁)and the amount of insulation in inches (X₂).Given below is EXCEL output of the regression model. Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672 -True or False: When an explanatory variable is dropped from a multiple regression model,the coefficient of multiple determination can increase.

TABLE 14-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y).To provide its customers with information on that matter,a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁)and the amount of insulation in inches (X₂).Given below is EXCEL output of the regression model. Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672 -True or False: You have just computed a regression model in which the value of coefficient of multiple determination is 0.57.To determine if this indicates that the independent variables explain a significant portion of the variation in the dependent variable,you would perform an F test.

TABLE 14-4 A real estate builder wishes to determine how house size (House)is influenced by family income (Income)and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: Also SSR (X₁ ∣ X₂)= 36400.6326 and SSR (X₂ ∣ X₁)= 3297.7917 -Referring to Table 14-4,suppose the builder wants to test whether the coefficient on Size is significantly different from 0.What is the value of the relevant t-statistic?

TABLE 14-13 An econometrician is interested in evaluating the relationship of demand for building materials to mortgage rates in Los Angeles and San Francisco.He believes that the appropriate model is Y = 10 + 5X₁ + 8X₂ where X₁ = mortgage rate in % X₂ = 1 if SF,0 if LA Y = demand in $100 per capita -Referring to Table 14-13,holding constant the effect of city,each additional increase of 1% in the mortgage rate would lead to an estimated increase of ________ in the mean demand.

TABLE 14-16 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 30 different vehicle models were collected: Y (Accel Time): Acceleration time in sec. X₁ (Engine Size): c.c. X₂ (Sedan): 1 if the vehicle model is a sedan and 0 otherwise The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of partial determinations and are 0.3301,and 0.0594,respectively. The coefficient of determination for the regression model using each of the 2 independent variables as the dependent variable and the other independent variable as independent variables ( )are,respectively 0.0077,and 0.0077. -True or False: Referring to Table 14-16,the 0 to 60 miles per hour acceleration time of a sedan is predicted to be 0.0005 seconds lower than that of a non-sedan with the same engine size.

TABLE 14-6 One of the most common questions of prospective house buyers pertains to the cost of heating in dollars (Y).To provide its customers with information on that matter,a large real estate firm used the following 2 variables to predict heating costs: the daily minimum outside temperature in degrees of Fahrenheit (X₁)and the amount of insulation in inches (X₂).Given below is EXCEL output of the regression model. Also SSR (X₁ ∣ X₂)= 8343.3572 and SSR (X₂ ∣ X₁)= 4199.2672 -Referring to Table 14-6,what is the 95% confidence interval for the expected change in heating costs as a result of a 1 degree Fahrenheit change in the daily minimum outside temperature?

TABLE 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000)and 2 variables: age (X₁ = Age)and experience in the field (X₂ = Exper).He took a sample of 20 employees and obtained the following Microsoft Excel output: Also,the sum of squares due to the regression for the model that includes only Age is 5022.0654 while the sum of squares due to the regression for the model that includes only Exper is 125.9848. -Referring to Table 14-8,the critical value of an F test on the entire regression for a level of significance of 0.01 is ________.

TABLE 14-16 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 30 different vehicle models were collected: Y (Accel Time): Acceleration time in sec. X₁ (Engine Size): c.c. X₂ (Sedan): 1 if the vehicle model is a sedan and 0 otherwise The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of partial determinations and are 0.3301,and 0.0594,respectively. The coefficient of determination for the regression model using each of the 2 independent variables as the dependent variable and the other independent variable as independent variables ( )are,respectively 0.0077,and 0.0077. -Referring to Table 14-16,which of the following assumptions is most likely violated based on the normal probability plot?

TABLE 14-3 An economist is interested to see how consumption for an economy (in $ billions)is influenced by gross domestic product ($ billions)and aggregate price (consumer price index).The Microsoft Excel output of this regression is partially reproduced below. -Referring to Table 14-3,what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premiums depend very much on the age of the individual and the number of traffic tickets received by the individual.You performed a regression analysis in EXCEL and obtained the following partial information: -If a categorical independent variable contains 4 categories,then ________ dummy variable(s)will be needed to uniquely represent these categories.

TABLE 14-15 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),mean teacher salary in thousands of dollars (Salaries),and instructional spending per pupil in thousands of dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable,X₁ = Salaries and X₂ = Spending: -True or False: Referring to Table 14-15,you can conclude definitively that mean teacher salary individually has no impact on the mean percentage of students passing the proficiency test,taking into account the effect of that instructional spending per pupil,at a 10% level of significance based solely on but not actually computing the 90% confidence interval estimate for β₁.

TABLE 14-15 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),mean teacher salary in thousands of dollars (Salaries),and instructional spending per pupil in thousands of dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable,X₁ = Salaries and X₂ = Spending: -True or False: Referring to Table 14-15,the null hypothesis H₀ : β₁ = β₂ = 0 implies that percentage of students passing the proficiency test is not related to either of the explanatory variables.

TABLE 14-4 A real estate builder wishes to determine how house size (House)is influenced by family income (Income)and family size (Size).House size is measured in hundreds of square feet and income is measured in thousands of dollars.The builder randomly selected 50 families and ran the multiple regression.Partial Microsoft Excel output is provided below: Also SSR (X₁ ∣ X₂)= 36400.6326 and SSR (X₂ ∣ X₁)= 3297.7917 -Referring to Table 14-4,the partial F test for H₀ : Variable X₁ does not significantly improve the model after variable X₂ has been included H₁ : Variable X₁ significantly improves the model after variable X₂ has been included has ________ and ________ degrees of freedom.

TABLE 14-10 You worked as an intern at We Always Win Car Insurance Company last summer.You notice that individual car insurance premiums depend very much on the age of the individual and the number of traffic tickets received by the individual.You performed a regression analysis in EXCEL and obtained the following partial information: -Referring to Table 14-10,to test the significance of the multiple regression model,what are the degrees of freedom?

TABLE 14-15 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),mean teacher salary in thousands of dollars (Salaries),and instructional spending per pupil in thousands of dollars (Spending)of 47 schools in the state. Following is the multiple regression output with Y = % Passing as the dependent variable,X₁ = Salaries and X₂ = Spending: -Referring to Table 14-15,which of the following is a correct statement?

TABLE 14-16 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 30 different vehicle models were collected: Y (Accel Time): Acceleration time in sec. X₁ (Engine Size): c.c. X₂ (Sedan): 1 if the vehicle model is a sedan and 0 otherwise The regression results using acceleration time as the dependent variable and the remaining variables as the independent variables are presented below. The various residual plots are as shown below. The coefficient of partial determinations and are 0.3301,and 0.0594,respectively. The coefficient of determination for the regression model using each of the 2 independent variables as the dependent variable and the other independent variable as independent variables ( )are,respectively 0.0077,and 0.0077. -Referring to Table 14-16,what is the p-value of the test statistic to determine whether engine size makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance?

TABLE 14-18 A logistic regression model was estimated in order to predict the probability that a randomly chosen university or college would be a private university using information on mean total Scholastic Aptitude Test score (SAT)at the university or college and whether the TOEFL criterion is at least 90 (Toefl90 = 1 if yes,0 otherwise).The dependent variable,Y,is school type (Type = 1 if private and 0 otherwise). The PHStat output is given below: -Referring to Table 14-18,what is the estimated odds ratio for a school with a mean SAT score of 1250 and a TOEFL criterion that is at least 90?