MAT 240 Module Three Assignment-Gardner

1 Housing Price Prediction Model for D.M. Pan National Real Estate Company Devan Gardner Department of Math, Southern New Hampshire University MAT 240: Applied Statistics Jody Tate January 28, 2024

2 Housing Price Prediction Model for D.M. Pan National Real Estate Company Module Two Notes Region State County listing price $'s per square foot square feet New England ma norfolk 394,600 $202 1,949 New England ri washington 360,700 $183 1,971 New England ri kent 397,900 $165 2,405 New England me kennebec 331,100 $165 2,005 New England ma franklin 385,200 $171 2,247 New England nh belknap 357,600 $178 2,013 New England me cumberland 370,700 $213 1,744 New England nh hillsborough 372,300 $185 2,014 New England ct fairfield 299,700 $167 1,798 New England ri providence 379,100 $148 2,566 New England ri bristol 355,100 $206 1,726 New England ct new haven 387,100 $181 2,142 New England ct tolland 378,100 $187 2,018 New England ma worcester 395,800 $176 2,246 New England vt chittenden 340,300 $183 1,855 New England ri washington 357,800 $181 1,975 New England ri newport 402,200 $157 2,556 New England ma barnstable 351,800 $143 2,455 New England ma essex 391,300 $179 2,183 New England ma suffolk 853,700 $143 5,987 New England ct litchfield 339,000 $190 1,780 New England nh grafton 373,800 $175 2,131 New England vt chittenden 560,900 $136 4,128 New England me cumberland 347,900 $145 2,403 New England ct middlesex 347,000 $157 2,214 New England nh merrimack 305,500 $166 1,843 New England vt windsor 731,000 $137 5,319 New England ma berkshire 422,800 $168 2,511 New England ma norfolk 313,400 $174 1,806 New England me androscoggin 333,600 $166 2,015   listing price National List price Mean 397900 342365 Median 371500 318000 Standard Deviation 117934 125914 square feet National Sq Ft Mean 2400 2111 Median 2075 1881 Standard Deviation 993 921

4 Examine the Slope and Intercepts Slope= 115.42 Intercept= 120863 The slope represents the increase in price as the square footage increases. The intercept represents the starting value of a home at 0 square feet. In the regression equation, we multiply the square footage of the home with the slope (115.42) and add that to the intercept (120863). R-squared Coefficient The R-squared value of 0.945227147 means that 94% of the variation in the listing price can be explained by changes in the square footage of homes in the New England region. It demonstrates that there is a strong, positive correlation between the size of a home and its listing price, confirming that larger homes tend to lead to higher listing prices. Conclusions The information I’ve provided in this prediction model underscores a strong positive correlation between square footage and listing price in the New England region. The correlation coefficient (r) of 0.972227929 signifies a highly significant linear relationship, and the regression model's slope (115.42) indicates that, on average, listing prices increase by $115.42 for each additional square foot. The intercept of 120,863 suggests the starting value of a home with zero square footage. There would be no correlation at zero because one would not sell a 0 square foot house. The R-squared value of 0.945227147 further explains the predictive power of the model, showing 94% of the variation in listing prices based on changes in square footage. My analysis provides important statistics for listing prices, cost per square foot, and square footage in both New England and the entire United States. In New England, the average

5 listing price is $397,90, with a cost of $171 per square foot and an average square footage of 2,400. There is a clear positive connection between square footage and listing prices. When comparing these numbers to U.S. homes overall, both datasets show similar average and middle values, indicating a consistent relationship between square footage and sales price across the country. However, there could still be some regional differences, as New England skews a little higher than the national average. The regression equation (Y = 115.42x + 120863) serves as a practical tool for our team of real estate professionals to estimate listing prices based on square footage. This gives our team better information to facilitate our listings. The data suggests that larger homes tend to see higher listing prices in the New England region and provides valuable guidance for our teams working in that real estate market.