MAT 240 Module Three Assignment Joshua Rivera

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Selling Price and Area Analysis for D.M. Pan National Real Estate Company 1 Report: Selling Price and Area Analysis for D.M. Pan National Real Estate Company Joshua Rivera Southern New Hampshire University

Selling Price Analysis for D.M. Pan National Real Estate Company 2 Introduction Hired as a junior analyst by D.M. Pan Real Estate Company, I’ve been tasked with preparing a report that examines the relationship between the selling price of properties and their size in square feet. For this examination, I’ve selected a random sample of 30 from the East North Central region to conduct a complete initial analysis report to provide to the team. Representative Data Sample East North Central Square Feet Listing Price 1,693 278,700 1,307 163,000 2,081 218,300 1,986 256,700 1,688 207,500 1,493 225,300 1,789 226,200 2,033 226,400 1,201 139,200 1,463 154,300 1,230 201,000 1,783 197,600 1,294 181,400 1,666 184,900 2,014 243,200 1,157 174,500 2,081 324,400 1,692 236,700 1,752 240,500 1,853 265,700 1,978 270,600 1,494 192,400 1,777 222,500 1,651 221,600 1,441 203,800 1,550 227,600 1,416 160,800

Selling Price Analysis for D.M. Pan National Real Estate Company 3 3,581 461,400 1,676 225,900 1,434 187,900 Square Feet Listing Price mean median standard deviation mean median standard deviation 1,708 1,682 443.8321159 224,000 222,050 60186.06208 Data Analysis The regional sample created shows only 3% of the national market. Comparing the regional sample with the national sample, the trend is very similar. In both samples, the larger the square feet, the higher the price of the home. In contrast, the 3% of the regional sample does not accurately represent the overall mean of square feet and home prices. The national average homes are approximately $100,000 higher than the regional sample; and the square feet is 400 greater than the ladder. To get a random regional sample, I randomized all 100 of the East North Central region homes using excel macros then selected the first 30 samples to chart. To get a truly random sample for the East North Central region, I would have used all 100 samples to better represent the national population, increasing it from 3% to 10%. Scatterplot

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Selling Price Analysis for D.M. Pan National Real Estate Company 4 Regression Equation: y=121.53x + 16362 R= 0.896238 Strength: Strong Direction: Positive R is the denotation of correlation. Correlation is the association between two variables. In this case, the correlation is positive, meaning when the square feet of a home increases, the listing price increases alongside it. This correlation is strong because 0.896238 is very close to 1; anything below 0.80 would be considered moderate. The slope is 121.53. This means that when, for example, the square feet increase by 500, the price of the home would increase to $60,765. The Y intercept is 16362. This means that when the regression line passes through the y axis, it would land on $16,362. $16,362 at 0 square feet. This would be the price of the land. Since we are calculating prices of homes and not of land, these observations wouldn’t make sense here. Also, since the house with the lowest square feet falls between 1,000 and 1,125, observing values at 0 square feet would be irrelevant. R 2 is 0.8032. R2 is the coefficient of determination. This measures how accurately the regression line follows the pattern of the data. The closer the value to 1, or 100%, the more accurate it is. The 0.896238 means that 90% of the variation in listing price can be explained by the variation in square feet.

Selling Price Analysis for D.M. Pan National Real Estate Company 5 The square footage of homes from the region selected compared to the square footage of homes in the U.S. is different. When it comes to MEAN, MEDIAN, STANDARD DEVIATION, Q1, Q3, and MAX, the East North Central region is lower apart from MIN, which is only 56 square feet higher. Using the slope, if the square footage were to go by 100 square feet, we can expect the price to increase by $12,153. We would want to use the square footage range within the range of data points which are approximately 1,100 square feet and 3,581 square feet; between the MIN and MAX. The Pattern Based on the graph, the “Listing Price” is the response variable (y), and the “Square Feet” is the predictor variable (x). In this case, the number of square feet a home has would determine the price range, making it useful for predictions. According to the trend, the larger the square feet (x), the higher the price (y). The shape of the scatterplot is linear. There is one outlier. This outlier represents a home with a price and square footage much higher than the sample average. Of the 100 of the East North Central homes, prices range from $135,300 - $581,800 and square feet range from 1,113 – 5,146. Taking a simple random sample of 30 may not accurately reflect the wide set of values from the original 100. If I had an 1,800 square foot house, it would go for approximately $235,116 according to the regression line and equation. A common use for these regression lines is to make predictions based on the patterns.

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