Exam 14: Introduction to Multiple Regression

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 value of the test statistic to determine whether being a sedan or not makes a significant contribution to the regression model in the presence of the other independent variable at a 5% level of significance?

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,the value of the test statistic is ________.

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: The coefficient of multiple determination measures the proportion of variation in Y that is explained by X₁ and X₂.

TABLE 14-12 As a project for his business statistics class,a student examined the factors that determined parking meter rates throughout the campus area.Data were collected for the price ($)per hour of parking,blocks to the quadrangle,and whether the parking is on or off campus.The population regression model hypothesized is Y_i = α + β₁X_1i + β₂X_2i + ε where Y is the meter price per hour. X₁ is the number of blocks to the quad. X₂ is a dummy variable that takes the value 1 if the meter is located on campus and 0 otherwise. The following Excel results are obtained. -True or False: In trying to construct a model to estimate grades on a statistics test,a professor wanted to include,among other factors,whether the person had taken the course previously.To do this,the professor included a dummy variable in her regression model that was equal to 1 if the person had previously taken the course,and 0 otherwise.The interpretation of the coefficient associated with this dummy variable would be the mean amount the repeat students tended to be above or below non-repeaters,with all other factors the same.

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.She proceeds to randomly select 26 large corporations and record information in millions of dollars.The Microsoft Excel output below shows results of this multiple regression. -Referring to Table 14-5,one company in the sample had sales of $21.439 billion (Sales = 21,439).This company spent $300 million on capital and $700 million on wages.What is the residual (in millions of dollars)for this data point?

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,the effect of living in San Francisco rather than Los Angeles is to increase the mean demand by an estimated ________.

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 estimated mean consumption level for an economy with GDP equal to $2 billion and an aggregate price index of 90?

TABLE 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income,in thousands of dollars)and lawn size (Lawn Size,in thousands of square feet). The PHStat output is given below: -Referring to Table 14-19,what is the p-value of the test statistic when testing whether Income makes a significant contribution to the model in the presence of LawnSize?

TABLE 14-7 The department head of the accounting department wanted to see if she could predict the GPA of students using the number of course units (credits)and total SAT scores of each.She takes a sample of students and generates the following Microsoft Excel output: -Referring to Table 14-7,the department head wants to use a t test to test for the significance of the coefficient of X₁.For a level of significance of 0.05,the critical values of the test are ________.

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 should be rejected at a 5% level of significance when testing whether instructional spending per pupil has any effect on percentage of students passing the proficiency test,taking into account the effect of mean teacher salary.

TABLE 14-5 A microeconomist wants to determine how corporate sales are influenced by capital and wage spending by companies.She proceeds to randomly select 26 large corporations and record information in millions of dollars.The Microsoft Excel output below shows results of this multiple regression. -Referring to Table 14-5,what is the p-value for testing whether Capital has a positive influence on corporate sales?

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,estimate the mean percentage of students passing the proficiency test for all the schools that have a mean teacher salary of 40,000 dollars,and an instructional spending per pupil of 2,000 dollars.

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 instructional spending per pupil individually has no impact on the mean percentage of students passing the proficiency test,taking into account the effect of mean teacher salary,at a 1% level of significance based solely on but not actually computing the 99% the confidence interval estimate for β₂.

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 that instructional spending per pupil has no impact on the mean percentage of students passing the proficiency test,taking into account the effect of mean teacher salary,at a 5% level of significance using the confidence interval estimate for β₂.

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,there is sufficient evidence that at least one of the explanatory variables is related to the number of weeks a worker is unemployed due to a layoff at a 10% level of significance.

TABLE 14-11 A weight-loss clinic wants to use regression analysis to build a model for weight loss of a client (measured in pounds).Two variables thought to affect weight loss are client's length of time on the weight-loss program and time of session.These variables are described below: Y = Weight loss (in pounds) X₁ = Length of time in weight-loss program (in months) X₂ = 1 if morning session,0 if not Data for 25 clients on a weight-loss program at the clinic were collected and used to fit the interaction model: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₁X₂ + ε Output from Microsoft Excel follows: -True or False: Referring to Table 14-11,the overall model for predicting weight loss (Y)is statistically significant at the 0.05 level.

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: A regression had the following results: SST = 82.55,SSE = 29.85.It can be said that 63.84% of the variation in the dependent variable is explained by the independent variables in the regression.

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 1100 and a TOEFL criterion that is not at least 90?

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,what is the value of the test statistic to determine whether there is a significant relationship between percentage of students passing the proficiency test and the entire set of 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,what annual income (in thousands of dollars)would an individual with a family size of 9 need to attain a predicted 5,000 square foot home (House = 50)?