Exam 17: Regression Models With Dummy Variables

In a model y = β₀ + β₁x + β₂d + β₃xd + ε, the ________ F test for the joint significance of d and xd can be performed.

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 binary variable with 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. Which of the following is the estimated regression 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. Suppose that at the 5% significance level you do not reject the null hypothesis, H₀: β₁ = β₃ = 0, when testing the joint significance of Time and Time × Prime in Model B. Should you delete both Time and Time × Prime from Model B?

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

A medical researcher is interested in assessing the probability of some symptoms of coronary heart disease (CHD) being present at a given age. For this reason, he uses the following data collected on 100 individuals. The response variable is CHD which is 1 if coronary heart disease is present and 0 otherwise. The following linear probability model and logit model have been estimated: Linear probability: = - 0.53796 + 0.02181Age Logit: = Using the linear probability model, what is the estimated probability of coronary heart disease for a 60-year-old individual?

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 + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε Using Model B, what is the regression equation found by Excel for females?

A logit model can be estimated with the method of ________.

Consider the model y = β₀ + β₁x + β₂d + ε, where x is a quantitative variable and d is a dummy variable. When d = 1, the predicted value of y ________.

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.

A logit model ensures that the predicted probability of the binary response variable falls between ________.

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

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 summer days?

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. To estimate this probability, she decided to use the logit model, P = , where y = a binary response variable which is 1 if the credit card is in default and 0 otherwise x₁ = the ratio of the credit card balance to the credit card limit (in %) x₂ = the ratio of the total debt to the annual income (in %) The following output is obtained. Note: The p-values of the corresponding tests are shown in parentheses below the estimated coefficients. Assuming the debt ratio is 30%, what is the range of values for the balance ratio that yields the fair rating?

If the number of dummy variables representing a qualitative variable equals the number of categories of this variable, one deals with the problem of perfect multicollinearity.

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 + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε A group of female managers considers a discrimination lawsuit if on average their salaries can be statistically proven to be lower by more than $500 than the salaries of their male peers with the same level of education and experience. Using Model B, what is the alternative hypothesis for testing the lawsuit condition?

For the model y = β₀ + β₁x + β₂d + ε, which test is used for testing the significance of a dummy variable d?

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. The Excel partial outputs corresponding to these models are available and shown below. Model A: Salary = β₀ + β₁Educ + β₂Exper + β₃Train + β₄Gender + ε Model B: Salary = β₀ + β₁Educ + β₂Exper + β₃Gender + ε A group of female managers considers a discrimination lawsuit if on average their salaries could be statistically proven to be lower by more than $500 than the salaries of their male peers with the same level of education and experience. Using Model B, what is the conclusion of the appropriate test at 10% significance level?

A model y = β₀ + β₁x + ε, in which y is a binary variable, is called a linear probability model.

Regression models that use a dummy variable as the response variable are called binary or discrete ________ models.

A medical researcher is interested in assessing the probability of some symptoms of coronary heart disease being present at a given age. For this reason, he uses the following data collected on 100 individuals. The response variable is CHD which is 1 if coronary heart disease is present and 0 otherwise. The following linear probability model and logit model have been estimated: Linear probability: = - 0.53796 + 0.02181Age Logit: = Using the linear probability model, find the age of a person for which the estimated chances of having coronary heart disease are 50%?