Quantitative Methods Practice Final Exam
Q1. The IRS wants to develop a method for detecting whether or not individuals have overstated their deductions for charitable contributions in their tax returns. The data in the Question #1 tab shows the adjusted gross income (AGI) and charitable contributions of 11 taxpayers whose returns were audited and found to be correct.
a. Does there appear to be a linear relationship between AGI and charitable contributions?
b. Develop a linear regression model that can be used to estimate the level of charitable contributions from a return's AGI. A taxpayer files a return with an AGI of $75,000 and charitable contributions of $12,000. Does the regression model identify this return as one with an unusually high charitable contribution?
Q2. The owner of a car lot that specializes in used Corvettes wants to develop a model to predict the expected selling prices. He collected the data in the Question #2 tab to build the model. The data includes selling price, mileage (in thousands), year, and the presence or absence of a T-top.
a. In a regression model with all the variables, does the year help to explain the selling price of the cars if the mileage is also in the model?
b. In a regression model with mileage and T-top as the only explanatory variables, what is the difference between a car with and without a T-top?
c. According to the regression model in part b), what is the estimated price difference for a mileage difference of 10,000 miles.
d. It has been suggested that the relationship between mileage and price is not linear. Would adding squared-mileage as an explanatory variable improve the regression model in part b?
Q3. The data in the Question #3 tab represents quarterly sales of sport utility vehicles sold by a local car dealer during the past three years. Use regression analysis to forecast sales for each quarter of 2016.
Q4. A computer company sets sales quotas for all salespeople based on their territory. To set fair sales quotas, the computer company needs a way to estimate computer sales in each territory, accounting for the fact that territories have different populations. From the 2011 Pocket World in Figures by the Economist, you can obtain the data in the Question #4 tab that includes, for a list of European countries, population (in millions), computer sales (in millions of U.S. dollars), sales per capita (in U.S. dollars), GNP per capita, average unemployment rate, and percentage of GNP spent in education. Use this cross-sectional data to find the best regression model to estimate sales per capita in a territory, i.e., a country.
Q5. Wireless Magazine is interested in determining whether the choice of mobile phone carrier depends on the customer type. In particular, the magazine is interested in three types of customers: families, individuals, or corporations. A sample of 150 customers is shown in the Question #5 tab. Each observation consists of the customer type and the carrier. Is the choice of carrier independent of customer type?
Q6. For a gender discrimination case, a lawyer wants to build a model that can show that, accounting for all relevant factors, over a period of time, salaries for female employees lag behind those of male employees. Her hypothesis is that the difference is of at least 30% and she would like to prove it. She has collected a sample of 200 employees, where each observation includes, gender, level of education, experience, job level, starting salary, and current salary. Instead of simply averaging the salary increases for men and for women and calculating an average difference, the lawyer wants to build a regression model in order to account for the relevant factors (that is, levels of education, job levels, and amount of experience). Develop a regression model that can help the lawyer detect significant differences in current salaries. Does the model support the lawyer's claim? (Hint: Create an interaction variable by multiplying Gender and Starting salary. Then develop a model with Education, Experience, Job Level, and the interaction variable.)
Attachment:- Assignment Files.rar