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 to estimate gpa.
(b) (10) What is the expected sign of each
coefficient? Why?
(c) (5) Describe how the
admissions office could use your model to admit only the students with the
highest predicted performance and the university could use your model to
identify students that may need help with their course work.
(d) (5) Suppose I wanted to identify students
that weren’t performing to their best ability. How could I use your model?
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