2023 FALL Project _ updated (1)
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School
Community College of Baltimore County *
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Course
153
Subject
Mathematics
Date
Jan 9, 2024
Type
Pages
1
Uploaded by AdmiralKnowledgePony26 on coursehero.com
Math 153 Project
In this project, we use a data set describing the sale of individual residential property in Ames, Iowa
from 2006 to 2010 from Cock [1]. The data set contains 2930 observations and a large number of
explanatory variables (23 nominal, 23 ordinal, 14 discrete, and 20 continuous) involved in assessing
home values. The link to the data set can be found
here
(https://www.statcrunch.com/app/index.html?dataid=3998101#).
The variables of our interest are listed below.
Variable
Description
Price
Sale price in USD.
Area
Above grade (ground) living area square feet.
Neighborhood
Physical locations within Ames city limits (map available).
Bldg.Type
Type of dwelling.
House.Style
Style of dwelling.
Year.Built
Original construction date.
Overall.Qual
Rates the overall material and finish of the house.
Overall.Cond
Rates the overall condition of the house.
Full.Bath
Full bathrooms above grade.
Half.Bath
Half baths above grade.
Fireplaces
Number of fireplaces.
Yr.Sold
Year Sold (YYYY).
Use this data set to answer the following questions.
1.
Calculate the mean, median, standard deviation and interquartile range (IQR) for the Price
column. Also, draw the histogram to display the distribution of this variable.
2.
Calculate the relative frequency for different categories of the Bldg.Type column. Also, draw the
bar graph to display the distribution of this variable.
3.
Draw the scatter plot for the bivariate data collected for Area and Price. Which of these two
variables is the response variable? Which is the explanatory variable? Determine the least-
squares regression line for the relation between these two variables. Interpret the meaning of
slope within the context.
4.
Suppose one property is randomly selected from this data set.
a.
What is the probability that this property is a single family home?
b.
What is the probability that this property is a single family home given that it is in the
Somerset (Somerst in the data) neighborhood of Ames?
5.
Create side-by-side boxplots for the sales price of properties with different numbers of full
bathrooms above grade. Be sure to give a few sentences comparing the similarities and
differences of sales price for different categories.
6.
Create a 95% confidence interval for the mean sales price of individual residential property in
Ames, Iowa from 2006 to 2010. Be sure to include a statement interpreting the confidence
interval result within the context.
7.
Are the mean sales prices different between the Somerst and Gilbert neighborhoods? Use a
0.05 significance level to determine this. Be sure to demonstrate all steps of the hypothesis
testing process. Hint: Summary statistics for Price can be calculated in StatCrunch with Group
by Neighborhood. Alternatively, Two Sample T test can be conducted in StatCrunch with Price
data Where: Neighborhood=Somerst for one sample and Where: Neighborhood=Gilbert for the
other sample.
Reference:
Ames, Iowa: Alternative to the Boston Housing Data as an End of Semester Regression Project.
Dean De Cock, Truman State University, Journal of Statistics Education, Volume 19, Number 3(2011),
www.amstat.org/publications/jse/v19n3/decock.pdf
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