BUSA542 - Regression Analysis: Predicting Investment Returns & Costs

This assignment focuses on regression analysis, featuring two main problems. The first problem involves developing a regression model to predict the annual rate of return for a stock based on its price-earnings (PE) ratio and risk measure, using data from Phidelity Investments. It requires preparing scatter plots, interpreting R-squared values for different models (linear and quadratic), and recommending the best model. The second problem addresses Caveat Emptor, Inc., a home inspection service, aiming to predict average monthly heating costs based on factors like outside temperature, attic insulation, furnace age, and house size. The tasks include creating scatter plots, identifying the best single, double, and triple independent variable models, determining the estimated regression function with all four variables, and developing a 95% prediction interval for heating costs, ultimately selecting the model with the highest adjusted R-squared statistic. The solution should be detailed, accurate, and correctly analyzed, with Excel tabs for solutions and models.

Assignment 6 – Regression Analysis
Fall 2018
The due date for the assignment 6 is 11/4/2018 (midnight). It must be submitted through the
“Assignment 6 – Regression Analysis” in Assignment Submission Folder provided in D2L. It is important
that you specify your name in the assignment document/attachment. The attachment name should
follow the following convention: BUSA542_ASSIGNMENT6_FIRSTNAME_LASTNAME.XLSX.
For each problem, please provide detail solution and written answers in a separate Excel tab. Your
model must be stored in different tab to get full credit:
1. An analyst for Phidelity Investments wants to develop a regression model to predict the
annual rate of return for a stock based on the price-earnings (PE) ratio of the stock and a
measure of the stock’s risk. Download the data from D2L to answer the following questions:
A. Prepare scatter plots for each independent variable versus the dependent variable. What
type of model do these scatter plots suggest might be appropriate for the data? (1 point)
B. Let Y = Return, X1 = PE Ratio, and X2 = Risk. Obtain the regression results for the following
regression model:
𝑌𝑖̂ = 𝑏0 + 𝑏1𝑋1𝑖 + 𝑏2𝑋2𝑖
Interpret the value of R2 for this model (1 point).
C. Obtain the regression results for the following regression model:
𝑌𝑖̂ = 𝑏0 + 𝑏1𝑋1𝑖 + 𝑏2𝑋2𝑖 + 𝑏3𝑋3𝑖 + 𝑏4𝑋4𝑖
Where 𝑋3𝑖 = 𝑋1𝑖
2 and 𝑋4𝑖 = 𝑋1𝑖
2 . Interpret the value of R2 for this model (1 point).
D. Which of the previous two models would you recommend that the analyst use? Explain
your reasons (1 point).
2. Caveat Emptor, Inc. is a home inspection service that provides prospective home buyers with
a thorough assessment of the major systems in a house prior to the execution of the
purchase contract. Prospective home buyers often ask the company for an estimate of the
average monthly heating cost of the home during the winter. To answer this question, the
company wants to build a regression model to help predict the average monthly heating cost
(Y) as a function of the average outside temperature in winter (X1), the amount of attic
insulation in the house (X2), the age of the furnace in the house (X3), and the size of the
house measured in square feet (X4). Download the data from D2L to answer the following
questions:
A. Prepare scatter plots showing the relationship between the average heating cost and
each of the potential independent variables. What sort of relationship does each plot
suggest? Explain your reasons (1 points).
B. If the company wanted to build a regression model using only one independent variable
to predict the average heating cost of these houses, what variable should be used?
Explain your reasons (1 points).

C. If the company wanted to build a regression model using only two independent variables
to predict the average heating cost of these houses, what variables should be use?
Explain your reasons (1 points).
D. If the company wanted to build a regression model using only three independent
variables to predict the average heating cost of these houses, what variables should be
use? Explain your reasons (1 points).
E. Suppose the company chooses to use the regression function with all four independent
variables. What is the estimated regression function? Explain your reasons (1 points).
F. Suppose the company decides to use the model with the highest adjusted R2 statistic.
Develop a 95% prediction interval for the average monthly heating cost of a house with 4
inches of attic insulation, a 5-year-old furnace, 2500 square feet, and in a location with
an average outside winter temperature of 40. Interpret this interval (1 points).
The following criteria will be used to grade the assignment:
Answers are detailed, accurate, and analysis are correct.
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Please feel free to consult your instructor by email or phone, if you have questions or need assistance!!