MAT 303 Project One Summary Report_ChinhDoan

MAT 303 Project One Summary Report CHINH DOAN chinh.doan@snhu.edu Southern New Hampshire University 1

1. Introduction As a data analyst employed by a real estate firm, I am tasked with analyzing a substantial historical data set pertaining to residential properties. The objective of this analysis is to examine the relationships among various attributes of homes. The findings from this analysis will be utilized to assist the real estate company in establishing more accurate pricing for their clients' property listings. The analytical methods employed in this project will encompass first order and second order regression models, involving both quantitative and qualitative variables, as well as a nested second order regression model. 2. Data Preparation The key variables included in this data set are price, age, square footage of the living area, number of bathrooms, view, square footage of the upper level, school rating, and crime rate. The data set consists of 2,692 individual records (rows) and encompasses 23 columns. 3. Model #1 - First Order Regression Model with Quantitative and Qualitative Variables 2

The scatterplot presented above illustrates a positive correlation between the price of a home and the square footage of its living area. Specifically, as the living area in square footage increases, there is a corresponding increase in the price of the home. 3

The scatterplot of the price compared to the age of the home exhibits a positive trend, indicating no association between the two variables. 4

The correlation coefficient between the price and the living area is 0.6895, while the correlation coefficient between the price and the age of the home is -0.0746. These values indicate a strong positive correlation between price and living area, and a strong negative correlation between price and the age of the home. Reporting Results: The general form and prediction equation of the multiple regression model is as follows: E ( y ) = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 + β 4 x 4 + β 5 x 5 R script: ^ y = 7709 + 129.3 x 1 + 19.51 x 2 + 1451 x 3 + 43970 x 4 + 1.67 ∗ 10 5 x 5 + e The multiple regression model is as follows: ^ y = ^ β 0 + ^ β 1 x 1 + ^ β 2 x 2 + ^ β 3 x 3 + ^ β 4 x 4 + ^ β 5 x 5 R script: ^ y = 77 09 + 129.3 x 1 + 19 . 51 x 2 + 1451 x 3 + 43970 x 4 + 2 . 49 ∗ 10 5 x 5 5