Housing Price Analysis for the Mountain Region Essay Sample (Term Paper Sample)

Module 3 Assignment:
Housing Price Analysis for the Mountain Region
Student’s Name
Institutional Affiliation
MODULE 3 ASSIGNMENT:
HOUSING PRICE ANALYSIS FOR THE MOUNTAIN REGION
This paper presents the analysis of the median price listing in the Mountain Region by exploring the relationship between the median price listing and the median square feet of the houses.
We use a sample of 30 observations from the Mountain Region to build a regression model with the Median Price listing as the dependent variable and the Median Square Feet as the independent variable. The correlation between these two variables is analyzed to get an understanding of how they relate. The regression model is analyzed by considering the R-squared metric so as to understand how much of the variation in the Median Price listing can be explained by the Median Square Feet of a house.
The model developed is used to make predictions of Median Price Listings given specified Median Square Feet.
Regression Equation
Using the Excel Data Analysis tool, we fit a linear regression model with the Median Square Feet as the independent variable,x and the Median Price Listing as the dependent variable, Y. The following out shows the coefficients for the fitted linear regression model:
The Linear Regression equation therefore is represented as follows:
Y=148254.74+112.63x
Where,
Y is the Median Price Listing
x is the Median Square Feet of the House
Correlation Coefficient, r
Determination of r
We determine the Correlation Coefficient, r, by using the correlation function of the Excel Data Analysis tool. The following is the correlation matrix output:
The Correlation Coefficient, r=0.34
Strength and Direction of Correlation
We note that the Correlation Coefficient is less than 0.5 which indicates a weak correlation between the two variables of Median Price Listing and Median Square Feet.
The Correlation Coefficient is greater than zero (positive) which indicates a positive correlation between the two variables. This implies that an increase in the Median Square Feet will have a corresponding increase in the Median Price Listing.
Analysis of the Regression Slop and Intercept
Interpretation of the Slop and Intercept
From the Linear Regression equation, the Slop, b1=112.63x and the intercept, b0=148254.74.
The Slop of the equation means that a one unit increase in the Median Square Feet will correspond to an increase in the Median Price Listing of $112.63.
The intercept indicates the value of the Median Price Listing when the Mean Squared Feet is zero. This does not practically make sense as a zero Mean Squared Feet means that there is no land and house available hence the Median Price should also be zero.
Determination of the Value of Land
If we interpreted the intercept to mean the price of the land only, this will mean that for the houses in the Mountain region, the Median Price of Land without a house is equal to $148,254.74.
Coefficient of Determination R-squared
The Coefficient of Determination for a linear regression with a single independent variable is given by, R2=r2, which is the square of the correlation coefficient:
R2=0.3415^2
R2=0.1166
R2=0.12
The R-squared value is a measure of goodness of fit which indicates how much variability in the dependent variable is explained by the independent variable.
In our case, the R-squared value of 0.12 indicates that about 12% of variation in the Median Price Listing can be explained by the Median Square Feet.
Analysis and Predictions
Square Foot for Homes in the Selected Region (Mountain Region)
We want to test if the square footage of homes in the selected region of Mountain is different than for the homes overall in the United States. Do test this, we will perform a one sample t-test on our sample data to compare the sample mean with the population mean for the square footage of the homes in overall United States.
From the given dataset, the mean footage for all the homes is, μ=1944.71. We want to test if the mean (M=2292.32) for our sample is statistically different from this population mean.
Given Data
Population Mean, μ=1944.71
Sample Mean, M=2292.32
Sample Standard Deviation, SD=80.74
Sample Size, n=30
Step 1: State Null and Alternative Hypothesis
H0:μ=1944.71, The square footage for homes in the Mountain Region is the same as the population mean of square footage for homes overall in the United States.
H1:μ≠1944.71, The square footage for homes in the Mountain Region is not the same as the population mean of square footage for homes overall in the United States.
Step 2: Select the Significance Level
We will test at a significance level of α=0.05
Step 3: Get the Test Statistics