Exam 17: Regression Models With Dummy Variables

Which of these represents a logistic regression model?

Exhibit 17.5.An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly 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 has been collected. Assuming the variables: Effectiveness = the response variable measured on a scale from 0 to 100, Age = the age of a patient (in years), Drug = a binary variable with 1 for the new drug,and 0 for the old drug,the regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug,is considered,and the following Excel results are available: Refer to Exhibit 17.5.What is the percentage of variations in Effectiveness explained by the estimated model?

Exhibit 17.5.An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly 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 has been collected. Assuming the variables: Effectiveness = the response variable measured on a scale from 0 to 100, Age = the age of a patient (in years), Drug = a binary variable with 1 for the new drug,and 0 for the old drug,the regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug,is considered,and the following Excel results are available: Refer to Exhibit 17.5.What is the estimated regression model?

Suppose that we have a qualitative variable Month with categories: January,February etc.How many dummy variables are needed to describe Month?

A dummy variable is commonly used to describe a quantitative variable with discrete or continuous values.

Exhibit 17.3.Consider the 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. Refer to Exhibit 17.3.What is the regression equation for the summer days?

Exhibit 17.8.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 + β₁Size + β₂Age + ε, Model B: Price = β₀ + β₁Size + β₂Loc1 + β₃Loc2 + ε, Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε, where, Price = the price of a home (in $thousands), Size = the square footage (in square 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. Refer to Exhibit 17.8.Using Model C,what is the alternative hypothesis for testing the significance of Age?

Exhibit 17.1.A researcher has developed the following regression equation to predict the prices of luxurious Oceanside condominium units, , where Price = the price of a unit (in $thousands), Size = the square footage (in square feet), View = a dummy variable taking on 1 for an ocean view unit,and 0 for a bay view unit. Refer to Exhibit 17.1.What is the predicted price of an ocean view unit with 1500 square feet?

Exhibit 17.8.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 + β₁Size + β₂Age + ε, Model B: Price = β₀ + β₁Size + β₂Loc1 + β₃Loc2 + ε, Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε, where, Price = the price of a home (in $thousands), Size = the square footage (in square 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. Refer to Exhibit 17.8.Using Model C,what is the null hypothesis for testing the joint significance of the two dummy variables?

Exhibit 17.4.A researcher wants to examine how the remaining balance on $100,000 loans taken 10-20 years ago depends on whether the loan was a prime or sub-prime loan.He collected a sample of 25 prime loans and 25 sub-prime loans and records the data in the following variables: Balance = the remaining amount of loan to be paid off (in dollars), Time = the time elapsed from taking the loan, Prime = a dummy variable assuming 1 for prime loans,and 0 for sub-prime 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 below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients. Refer to Exhibit 17.4.Using Model C,what is the predicted balance on a $100,000 sub-prime loan taken 15 years ago?

Exhibit 17.9.A bank manager is interested in assigning a rating to the holders of credit cards issued by her bank.The rating is based on the probability of defaulting on credit cards and is as follows.

Exhibit 17.9.A bank manager is interested in assigning a rating to the holders of credit cards issued by her bank.The rating is based on the probability of defaulting on credit cards and is as follows.

For the model y = β₀ + β₁x + β₂d + β₃xd + ε,in which d is a dummy variable,we cannot perform the F test for the joint significance of the dummy variable d and the interaction variable xd.

The logistic model can be estimated through the use of the ordinary least squares method.

Exhibit 17.5.An over-the-counter drug manufacturer wants to examine the effectiveness of a new drug in curing an illness most commonly 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 has been collected. Assuming the variables: Effectiveness = the response variable measured on a scale from 0 to 100, Age = the age of a patient (in years), Drug = a binary variable with 1 for the new drug,and 0 for the old drug,the regression model, Effectiveness = β₀ + β₁Age + β₂Drug + β₃Age × Drug,is considered,and the following Excel results are available: Refer to Exhibit 17.5.What is the estimated regression model for the new drug?

Exhibit 17.9.A bank manager is interested in assigning a rating to the holders of credit cards issued by her bank.The rating is based on the probability of defaulting on credit cards and is as follows.

Exhibit 17.4.A researcher wants to examine how the remaining balance on $100,000 loans taken 10-20 years ago depends on whether the loan was a prime or sub-prime loan.He collected a sample of 25 prime loans and 25 sub-prime loans and records the data in the following variables: Balance = the remaining amount of loan to be paid off (in dollars), Time = the time elapsed from taking the loan, Prime = a dummy variable assuming 1 for prime loans,and 0 for sub-prime 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 below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients. Refer to Exhibit 17.4.Using Model B,what is the value of the test statistic for testing the joint significance of the variable Time and the interaction variable Time × Prime?

Exhibit 17.8.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 + β₁Size + β₂Age + ε, Model B: Price = β₀ + β₁Size + β₂Loc1 + β₃Loc2 + ε, Model C: Price = β₀ + β₁Size + β₂Age + β₃Loc1 + β₄Loc2 + ε, where, Price = the price of a home (in $thousands), Size = the square footage (in square 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.

The number of dummy variables representing a qualitative variable should be one less than the number of categories of the variable.

Exhibit 17.2.To examine the differences between salaries of male and female middle managers of a large bank,90 individuals were randomly selected and 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. Also,the following Excel partial outputs corresponding to the following models are available: Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Refer to Exhibit 17.2.Using Model B,what is the regression equation found by Excel for females?