Exam 14: Introduction to Multiple Regression

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,the residual mean squares (MSE)that are missing in the ANOVA table should be ________.

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 fitted model for predicting demand in Los Angeles is ________.

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: -An interaction term in a multiple regression model may be used when

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: -Referring to Table 14-17,which of the following is a correct statement?

In a multiple regression model,the value of the coefficient of multiple determination

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 value of the partial F test statistic is ________ for H₀ : Variable X₂ does not significantly improve the model after variable X₁ has been included H₁ : Variable X₂ significantly improves the model after variable X₁ has been included

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,the value of the partial F test statistic is ________ for H_{0 :} 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

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: -Referring to Table 14-17,what is the p-value of the test statistic 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 14-18 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 probability that a school with a mean SAT score of 1250 and a TOEFL criterion that is at least 90?

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 are the predicted sales (in millions of dollars)for a company spending $500 million on capital and $200 million on wages?

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: When a dummy variable is included in a multiple regression model,the interpretation of the estimated slope coefficient does not make any sense anymore.

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: -Referring to Table 14-11,in terms of the βs in the model,give the mean change in weight loss (Y)for every 1 month increase in time on the program (X₁)when not attending the morning session.

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 is the predicted house size (in hundreds of square feet)for an individual earning an annual income of $40,000 and having a family size of 4?

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 analyst wants to use a t test to test for the significance of the coefficient of X₂.For a level of significance of 0.01,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 alternative hypothesis H₁ : At least one of β_j ≠ 0 for j = 1,2 implies that percentage of students passing the proficiency test is affected by at least one of the explanatory variables.

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

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 p-value of the test statistic when testing whether the model is a good-fitting model?

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,we can conclude definitively that,holding constant the effect of the other independent variable,age has an impact on the mean number of weeks a worker is unemployed due to a layoff at a 10% level of significance if all we have is the information of the 95% confidence interval estimate for the effect of a one year increase in age on the mean number of weeks a worker is unemployed due to a layoff.

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,the proportion of the total variability in insurance premiums that can be explained by AGE and TICKETS after adjusting for the number of observations and the number independent variables is ________.

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: -True or False: Referring to Table 14-7,the department head wants to use a t test to test for the significance of the coefficient of X₁.At a level of significance of 0.05,the department head would decide that β₁ ≠ 0.