2023 FALL Project _ updated (1)

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Community College of Baltimore County *

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153

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Mathematics

Date

Jan 9, 2024

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pdf

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1

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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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