Exam 17: Regression Models With Dummy Variables

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. What will be the rating for a person with a balance ratio of 15% and a debt ratio of 30%?

The major advantage of a logit model over a linear probability model is that the predicted values of y are always between ________.

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 rainy days?

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 difference in predicted prices of the ocean view and bay view units with the same square footage?

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

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 logit model, what is the estimated probability of coronary heart disease for a 60-year-old individual?

According to the Center for Disease Control and Prevention, life expectancy at age 65 in America is about 18.7 years. Medical researchers have argued that while excessive drinking is detrimental to health, drinking a little alcohol every day, especially wine, may be associated with the increase in life expectancy. Others have also linked longevity with income and gender. The data relating to the length of life after 65 (Life) were collected. Data were collected related to the length of life after 65 (Life) including the average income (in $1,000s) (Income), the average number of alcoholic drinks consumed per day (Drinks), and a dummy variable Woman which is 1 when the individual is a woman and 0 otherwise. The following model was created: Life = β₀ + β₁Income + β₂Drinks + β₃Woman + ε. Output corresponding to this model is shown below. Using a p-value approach, which of the following conclusions is correct at 5% significance level?

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. Suppose that at the 10% significance level, you do not reject the null hypothesis, H₀: β₂ = 0, when testing the significance of Age in Model C. Would you delete Age from Model C?

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. Which of the following is the estimated regression model for the new drug?

For the model y = β₀ + β₁x + β₂xd + ε, which of the following are the hypotheses for testing the individual significance of the interaction variable xd?

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

In the model y = β₀ + β₁x + β₂d + β₃xd + ε, for a given x and d = 1, the predicted value of y is given by ________.

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. Which of the following is the p-value for testing the individual significance of Time in Model B?

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. (Using Excel or R) Suppose that only applicants with excellent and good ratings are qualified for a loan. Assume that the balance ratio, x₁, of those who apply is normally distributed with μ₁ = 18% and σ₂ = 6%, while their debt ratio, x₂, is normally distributed with μ₂ = 30% and σ₂ = 8%. Assume also that x₁ and x₂ are independent. Simulate 1,000 applications to estimate the percent of those that are qualified for a loan.

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 obtained for the models are as follows: Model A: Salary = β₀ + β₁ Educ + β₂ Exper + β₃ Gender + β₄ Exper × Gender + ε, Model B: Salary = β₀ + β₁ Educ + β₂ Exper + ε, are summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients. Define the alternative hypothesis for testing the joint significance of Exper and Exper × Gender in Model A?

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 obtained for the models are as follows: Model A: Salary = β₀ + β₁ Educ + β₂ Exper + β₃ Gender + β₄ Exper × Gender + ε, Model B: Salary = β₀ + β₁ Educ + β₂ Exper + ε, are summarized in the following table. Note: The values of relevant test statistics are shown in parentheses below the estimated coefficients. What is the value of the test statistic for testing the joint significance of Exper and Exper × Gender in Model A?

Like any other university, Seton Hall University uses SAT scores and high school GPAs as primary criteria for admission. Data for 30 students who had recently applied to Seton Hall were collected including admission (1 for admission and 0 otherwise), SAT score, and GPA. Output for the model is shows below. Which of the following statements is correct about the individual significance of the variables at the 5% significance level?

Which of the following regression models does not include an interaction variable?

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 A, which of the following is the estimated average difference between the salaries of male and female employees with the same years of education, months of experience, and weeks of training?

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. What is the regression equation for model B?