Exam 17: Regression Models With Dummy Variables

Consider the regression equation = b₀ + b₁x + b₂d with a dummy variable d.If d increases from 0 to 1,the change in the intercept is given by:

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 winter rainy days?

Exhibit 17.7.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, Gender = the gender of an individual;1 for males,and 0 for females. The regression results for the models, Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + β₄Exper × Gender + ε, Model B: Salary = β₀ + β₁Educ + β₂Exper + ε,are summarized below.

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.For which age is the predicted effectiveness of the old and new dug is about the same?

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

For the model y = β₀ + β₁x + β₂d + β₃xd + ε,in which d is a dummy variable,we can perform standard t tests for the individual significance of x,d and xd.

Exhibit 17.7.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, Gender = the gender of an individual;1 for males,and 0 for females. The regression results for the models, Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + β₄Exper × Gender + ε, Model B: Salary = β₀ + β₁Educ + β₂Exper + ε,are summarized below.

Exhibit 17.7.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, Gender = the gender of an individual;1 for males,and 0 for females. The regression results for the models, Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + β₄Exper × Gender + ε, Model B: Salary = β₀ + β₁Educ + β₂Exper + ε,are summarized below.

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.Assuming the same temperature and precipitation condition,what is the difference between the predicted humidity for summer and winter days?

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 logistic model,the predicted values of the response variables can be always interpreted as probabilities.

Exhibit 17.7.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, Gender = the gender of an individual;1 for males,and 0 for females. The regression results for the models, Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + β₄Exper × Gender + ε, Model B: Salary = β₀ + β₁Educ + β₂Exper + ε,are summarized below. Note.The values of relevant test statistics are shown in parentheses below the estimated coefficients. Refer to Exhibit 17.7.What is the alternative hypothesis for testing the joint significance of Exper and Exper × Gender in Model A?

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.Which of the explanatory variables in Model A is most likely to be tested for the individual significance?

Consider the model y = β₀ + β₁x + β₂d + ε,where x is a quantitative variable and d is a dummy variable.We can use sample data to estimate the model as:

In the model y = β₀ + β₁x + β₂d + β₃xd + ε,when d changes from 0 to 1 how does the intercept of the corresponding lines change?

Which of the following predictions cannot be described by a binary choice model?

A binary choice model can be used,for example,to predict the chances of a candidate of winning an election.

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

For the model y = β₀ + β₁x + β₂d + β₃xd + ε,the dummy variable d causes only a shift in intercept.

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.