Exam 14: Introduction to Multiple Regression

SCENARIO 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, = Salaries and Spending: -Referring to Scenario 14-15, there is sufficient evidence that both of the explanatory variables are related to the percentage of students passing the proficiency test at a 5% level of significance.

SCENARIO 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, = Salaries and Spending: -Referring to Scenario 14-15, the alternative hypothesis : At least one of for j = 1, 2 implies that percentage of students passing the proficiency test is related to at least one of the explanatory variables.

SCENARIO 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 Scenario 14-3, what is the predicted consumption level for an economy with GDP equal to $4 billion and an aggregate price index of 150?

SCENARIO 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, = Salaries and Spending: -Referring to Scenario 14-15, there is sufficient evidence that instructional spending per pupil has an effect on percentage of students passing the proficiency test while holding constant the effect of mean teacher salary at a 5% level of significance.

SCENARIO 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 Scenario 14-17, which of the following is a correct statement?

SCENARIO 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, = Salaries and Spending: -Referring to Scenario 14-15, what is the p-value of the test statistic when testing whether mean teacher salary has any effect on percentage of students passing the proficiency test, considering the effect of instructional spending per pupil?

SCENARIO 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 Scenario 14-3, to test whether gross domestic product has a positive impact on consumption, the p-value is

SCENARIO 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 Scenario 14-3, when the economist used a simple linear regression model with consumption as the dependent variable and GDP as the independent variable, he obtained an value of 0.971.What additional percentage of the total variation of consumption has been explained by including aggregate prices in the multiple regression?

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.

SCENARIO 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 where -Referring to Scenario 14-13, the predicted demand in Los Angeles when the mortgage rate is 8% is ________.

SCENARIO 14-8 A financial analyst wanted to examine the relationship between salary (in $1,000)and 2 variables: age = Age)and experience in the field = 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 Scenario 14-8, the estimate of the unit change in the mean of Y per unit change in , considering the effects of the other variable, is ________.

SCENARIO 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 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 Scenario 14-16, the errors (residuals)appear to be right-skewed.

SCENARIO 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 Scenario 14-17, which of the following is the correct null hypothesis to test 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?

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.

SCENARIO 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 Scenario 14-10, the standard error of the estimate is _________.

SCENARIO 14-9 You decide to predict gasoline prices in different cities and towns in the United States for your term project.Your dependent variable is price of gasoline per gallon and your explanatory variables are per capita income and the number of firms that manufacture automobile parts in and around the city.You collected data of 32 cities and obtained a regression sum of squares SSR= 122.8821.Your computed value of standard error of the estimate is 1.9549. -Referring to Scenario 14-9, what is the value of the coefficient of multiple determination?

SCENARIO 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 where -Referring to Scenario 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.

SCENARIO 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 Scenario 14-10, the residual mean squares (MSE)that are missing in the ANOVA table should be _____.

SCENARIO 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 and the amount of insulation in inches Given below is EXCEL output of the regression model. -Referring to Scenario 14-6, the coefficient of partial determination is ____.

SCENARIO 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 Scenario 14-5, what is the p-value for testing whether Wages have a positive impact on corporate sales?