Question

**Part 1**

An important problem in real estate is determining how to price homes to be sold. There are so many factors—size, age, and style of the home; number of bedrooms and bathrooms; size of the lot; and so on—which makes setting a price a challenging task. In this project, we will try to help realtors in this task by determining how different characteristics of homes relate to home prices, identifying the key variables in pricing, and building multiple-variable regression models to predict prices based on property characteristics. Our analysis will be based on the Mount Pleasant Real Estate Data (available on stat.hawkeslearning.com). This data set includes information about 195 properties for sale in three communities in the suburban town of Mount Pleasant, South Carolina, in 2017. Consider the following variables associated with each property.

x |
x |

x |
x |

x |
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X |
x |

- Perform a hypothesis test to determine if the model is useful for predicting home values at a significance level of α = 0.05. State the followings:

- Determine the null and alternative hypotheses. (2 Points)
- What is the value of the test statistics (
*F*statistics)? (2 Points)

**65.****04884**

- Determine the
*P-value*. (2 Points) - Make a decision to reject or fail to reject
*H*. (2 Points)_{0} - State the conclusion in terms of the original question. (2 Points)

- Are any variables not useful predictors of home price at a
significance level of α = 0.05? State the
*P-values*of these variables. Intuitively, what does this mean with respect to pricing properties? (Show your results) (8 Points)

SUMMARY OUTPUT | ||||||||

Regression Statistics |
||||||||

Multiple R | 0.858306 | |||||||

R Square | 0.73669 | |||||||

Adjusted R Square | 0.725364 | |||||||

Standard Error | 94030.87 | |||||||

Observations | 195 | |||||||

ANOVA | ||||||||

df |
SS |
MS |
F |
Significance F |
||||

Regression | 8 | 4.6E+12 | 5.75E+11 | 65.04884 | 7.3335E-50 | |||

Residual | 186 | 1.64E+12 | 8.84E+09 | |||||

Total | 194 | 6.25E+12 |

Answer #1

Statistical Methods of Business II – Case Study –
Indiana Real Estate
Ann Perkins, a realtor in Brownsburg, Indiana, would like to use
estimates from a multiple regression model to help prospective
sellers determine a reasonable asking price for their homes. She
believes that the following four factors influence the asking price
(Price) of a house:
The square footage of the house (SQFT)
The number of bedrooms (Bed)
The number of bathrooms (Bath)
The lot size (LTSZ) in acres
She...

2: A real estate agent is interested in what factors determine
the selling price of homes in Northwest Arkansas. She takes a
random sample of 20 homes, and conducts a multiple regression
analysis. The dependent variable is price of the home (in thousands
of dollars), the square footage of the home, and whether the home
is located in a new subdivision (0 = no; 1 = yes). The results of
the multiple regression analysis are shown below. Answer the
following...

Homes For Sale
Data were collected from a random sample of 120 homes for sale
in the United States. The variables in the data set include the
following:
Price: asking price (in thousands of dollars)
Size: livable area (in thousands of square feet)
Beds: number of bedrooms
Bath: number of bathrooms
<Research Questions>
1. Is there a relationship between the size of a house and
asking price?
2. Can the asking price of a house be predicted using the size,...

The North Valley Real Estate data 2015 reports information on
homes on the market.
Let selling price be the dependent variable and size of the
home the independent variable. Determine the regression equation.
Estimate the selling price for a home with an area of 2,200 square
feet. Determine the 95% confidence interval for all 2,200 square
foot homes and the 95% prediction interval for the selling price of
a home with 2,200 square feet.
Let days-on-the-market be the dependent variable...

Nine homes are chosen at random from real estate listings in two
suburban neighborhoods, and the square footage of each home is
noted in the following table.
Size of Homes in Two Subdivisions
Subdivision
Square Footage
Greenwood
2,780
2,710
2,404
2,622
2,413
2,888
2,378
2,609
2,650
Pinewood
2,484
2,356
2,453
2,759
2,631
2,672
2,373
2,511
3,093
(a) Choose the appropriate hypothesis to test
if there is a difference between the average sizes of homes in the
two neighborhoods at the...

QUESTION 3
The managing director of a real estate company investigated how
advertising budget (in $000s) and number of agents affected annual
sales ($ million). He used data from 15 offices, and obtained the
following regression output:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.72
R Square
0.52
Adjusted R Square
0.44
Standard Error
7.36
Observations
15
ANOVA
df
SS
MS
F
Significance
Regression
2
716.58
358.29
6.61
0.01
Residual
12
650.35
54.20
Total
14
1366.93
Coefficients
Standard Error
t Stat...

1)A real estate agent
is interested in determining factors that affect the mean selling
price of a home. One factor she is considering is known as "lot
configuration," which determines the position of the house within
the neighborhood that it is built. The possible lot configurations
are (don't worry about their precise definitions):
Inside: Inside
lot
Corner: Corner
lot
CulDSac Cul-de-sac
FR2: Frontage
on 2 sides of property
FR3: Frontage
on 3 sides of property
Suppose that she were
to perform an ANOVA to examine...

Nine homes are chosen at random from real estate listings in two
suburban neighborhoods, and the square footage of each home is
noted in the following table.
Size of Homes in Two Subdivisions
Subdivision
Square Footage
Greenwood
2,312
2,471
2,490
2,892
2,341
2,412
2,830
2,723
2,350
Pinewood
2,600
2,494
2,558
2,816
2,391
2,574
2,558
2,854
3,466
(a) Choose the appropriate hypothesis to test
if there is a difference between the average sizes of homes in the
two neighborhoods at the...

A real estate builder wishes to determine how house size (House)
is influenced by family income (Income), family size (Size), and
education of the head of household (School). House size is measured
in hundreds of square feet, income is measured in thousands of
dollars, and education is in years. The builder randomly selected
50 families and ran the multiple regression. Microsoft Excel output
is provided below:
SUMMARY OUTPUT
Regression
Statistics
Multiple
R 0.865
R
Square 0.748
Adjusted R
Square 0.726
Standard
Error 5.195
Observations 50...

3. United Park City Properties real estate
investment firm took a random sample of five condominium units that
recently sold in the city. The sales prices Y (in thousands of
dollars) and the areas X (in hundreds of square feet) for each unit
are as follows
Y= Sales Price
( * $1000)
36
80
44
55
35
X = Area (square feet) (*100)
9
15
10
11
10
a. The owner wants to forecast sales on the basis of...

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