STAT 1430 Homework Solution
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1. (10 points) Given the equation y = β0 + β1x + . What does each part of the equation represent? (ie is the independent variable, etc)
2. (5 points) What is the difference between a residual and an error?
3. (10 points) In figure 1, the X’s represent data points x and y. The line represents a linear estimation of the relationship between x and y. Answer the following questions refering to the figure: (a) If the estimated equation is y = βˆ 0 + βˆ 1x + , what is the approximate value of βˆ 0? (b) What is the sign of βˆ 1? (c) What distance in the graph represents ˆ?
4. (20 points)You are working with a small firm that invests in real estate and have been charged with identifying homes that are priced below market value in Columbus. You are specifically looking at homes in Upper Arlington and have been able to collect the following data for homes sold in the past year: price, bedrooms, bathrooms, square footage of home, and square footage of lot.
(a) (5) Write out an equation that you could estimate with OLS. (ie wagei = β0 + β1educationi + β2agei + ....)
(b) (10) What is the expected sign of each coefficient? Why?
(c) (5) How could you use your model to identify homes that are currently underpriced?
5. (25 points) You were recently hired to work for the University. The university wants to improve their graduation rate. To do so they need to improve admissions and offer programs to help students that are in danger of failing to complete their degree in five years or less. They don’t have graduation data, but they do have each student’s college GPA, SAT score, high school GPA, High School rank among students (ie 1=valedictorian, 100 means 99 students in your class did better than you) and High School Standardized Test Percentile (0-100 where 100 means that your school is the best).
(a) (5) Write out an equation that you could use...