Exam 17: Regression Models With Dummy Variables

A realtor wants to predict and compare the prices of homes in three neighboring locations. She considers the following linear models: Model A: Price = β₀ + β₁ Size + β₂ Age + ε Model B: Price = β₀ + β₁ Size + β₃ Loc1 + β₄ Loc2 + ε Model C: Price = β₀ + β₁ Size + β₂ Age + β₃ Loc1 + β₄ Loc2 + ε where, Price = the price of a home (in $1,000s) Size = the square footage (in sq. feet) Loc1 = a dummy variable taking on 1 for Location 1, and 0 otherwise Loc2 = a dummy variable taking on 1 for Location 2, and 0 otherwise After collecting data on 52 sales and applying regression, her findings were summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients. Obtain the p-value for testing the individual significance of Age in Model C.

Gender is an example of ________ variable.

Consider the following regression model: Humidity = β₀ + β₁Temperature + β₂Spring + β₃Summer + β₄Fall + β₅Rain + ε, where the dummy variables Spring, Summer, and Fall represent the qualitative variable Season (spring, summer, fall, winter), and the dummy variable Rain is defined as Rain = 1 if rainy day, Rain = 0 otherwise. What is the regression equation for the winter rainy days?

To examine the differences between salaries of male and female middle managers of a large bank, 90 individuals were randomly selected, and two models were created with the following variables considered: Salary = the monthly salary (excluding fringe benefits and bonuses), Educ = the number of years of education, Exper = the number of months of experience, Train = the number of weeks of training, Gender = the gender of an individual; 1 for males, and 0 for females. Excel partial outputs corresponding to these models are available and shown below. Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃ Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Which of the following explanatory variables in Model A is not significant at the 5% level?

Which of the following predictions can be described by a binary choice model?

A researcher wants to examine how the remaining balance on $100,000 loans taken 10 to 20 years ago depends on whether the loan was a prime or subprime loan. He collected a sample of 25 prime loans and 25 subprime loans and recorded the data in the following variables: Balance = the remaining amount of loan to be paid off (in $), Time = the time elapsed from taking the loan, Prime = a dummy variable assuming 1 for prime loans, and 0 for subprime loans. The regression results obtained for the models: Model A: Balance = β₀ + β₁Prime + ε Model B: Balance = β₀ + β₁Time + β₂Prime + β₃Time × Prime + ε Model C: Balance = β₀ + β₁Prime + β₂Time × Prime + ε, Are summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients. Using Model B, what is the conclusion for testing the joint significance of the variable Time and the interaction variable Time × Prime at 5% significance level?

A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, = 40 + 0.15Size + 50View, where Price is the price of a unit (in $1,000s), Size is the square footage (in sq. feet), and View is a dummy variable taking on 1 for an ocean view unit and 0 for a bay view unit. Which of the following is the predicted price of a bay view unit measuring 1,500 square feet?

A realtor wants to predict and compare the prices of homes in three neighboring locations. She considers the following linear models: Model A: Price = β₀ + β₁ Size + β₂ Age + ε Model B: Price = β₀ + β₁ Size + β₃ Loc1 + β₄ Loc2 + ε Model C: Price = β₀ + β₁ Size + β₂ Age + β₃ Loc1 + β₄ Loc2 + ε where, Price = the price of a home (in $1,000s) Size = the square footage (in sq. feet) Loc1 = a dummy variable taking on 1 for Location 1, and 0 otherwise Loc2 = a dummy variable taking on 1 for Location 2, and 0 otherwise After collecting data on 52 sales and applying regression, her findings were summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients. Using Model B, compute the predicted price of a 2,500-square-foot home in Location 1.

An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly found in older patients. Thirteen patients are given the new drug and 13 patients are given the old drug. To avoid bias in the experiment, they are not told which drug is given to them. To check how the effectiveness depends on the age of patients, the following data have been collected. The variables are Effectiveness = the response variable measured on a scale from 0 to 100, Age = the age of a patient (in years), Drug = a dummy variable that is 1 for the new drug and 0 for the old drug. The regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug, is estimated and the following results are obtained. For which age is the predicted effectiveness of the old and new drug about the same?

Quantitative variables assume meaningful ________, whereas qualitative variables represent some ________.