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 foundhere (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. [10 points] Analyze the distribution of the following variables using the proper summary measures (mean/median/std dev/IQR/relative frequency/etc.) and graphs (histogram/boxplot/bar graph/pie chart/etc.). Do it separately for each variable.
   1. Price
   2. Bldg.Type
2. [25 points] 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.
3. [6 points] Suppose one property is randomly selected from this data set.
4. What is the probability that this property is a single family home?
5. 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?
6. 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 neighborhoods categories.
7. [10 points] 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.
8. [15 points] Is the type of dwelling (Variable: Bldg.Type) related to the year the property is sold (Variable: Yr.Sold)? Use a 0.01 significance level to determine this. Be sure to demonstrate all 5 steps of the hypothesis testing process.

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