MAT 240 Module Three Assignment
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Southern New Hampshire University *
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Feb 20, 2024
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Housing Price Prediction Model for D.M. Pan Real Estate Company
Karen Morrow
Southern New Hampshire University
MAT 240: Applied Statistics
Instructor Jennifer Turner
November 13, 2022
Median Housing Price Prediction Model for D.M. Pan National Real Estate Company
2
Module Two Notes
Median Housing Price Prediction Model for D.M. Pan National Real Estate Company
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Regression Equation
The regression equation for the line of best fit using the scatterplot is y= 124.08x +90127.
Determine r
It is determined that r equals 0.949965. “r” represents the correlation between the listing price and the square feet area. As the area of square feet increases, the listing price increases. Therefore, the association between the two variables is positive. This also explains why the correlation coefficient is positive. The correlation between the two variables is strong as it is closer to 1. Examine the Slope and Intercepts
The regression equation tells us that the slope is 124.08 and the intercept is 90127. The slope of 124.08 tells us that as the square feet area increases by one unit, then the listing price should increase by $124.08. The intercept is the point at which the regression line crosses the y-
axis when the x is zero. In this case, the y-intercept is going to be positive. The y-intercept tells us that when x (square feet area) is zero, y (listing price) should be positive 90127. In determining the value of the land, the assumption can be made that when the square footage of the house (x) is zero, the listing price (y) of $90,127 represents the land. This value does not make sense in context because the regression line only represents data for houses and does not include data for the land where there is no house built. The house with the lowest square
footage is 1,145 and because of that, we can only interpret the equation within the scope of this data. There is no doubt some value for the land on which the house is built; however, we do not have enough data to properly evaluate the price of the land itself.
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Median Housing Price Prediction Model for D.M. Pan National Real Estate Company
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R
-squared Coefficient
R-squared is the coefficient of determination that tells how the variation in the listing price is explained by the increase in the square feet area. R-squared (coefficient of determination) is found by squaring r (correlation). It has been determined that r = 0.949965; therefore, R-squared equals 0.902434 or 90%. This means that 90% of the variation in listing price is explained by variation in the square feet area and that data points will be much closer to the trend line. Some variation in the data will appear scattered around the regression line; however, the value will adjust accordingly. Conclusions
The charts below provide summary statistics on the square feet and listing prices for overall homes in the United States and homes in the Northeast region. Listing Price
National
Northeast
Mean
342365
301575.9
Std Dev
125914
76651.2
Min
135300
207,400
Q1
265250
257300
Median
318000
297,400
Q3
381600
315300
Max
987600
626,500
Square Feet
National
Northeast
Mean
2111
1,704
Std Dev
921
586.8486
Min
1101
1,145
Q1
1626
1407
Median
1881
1,574
Q3
2215
1881
Max
6516
4,354
The data in the charts allow comparisons of listing prices and square feet between the overall homes in the United States and homes in the Northeast region. While the minimum of both square feet and listing price for the Northeast region are higher than the national average, the overall square footage and listing prices for homes in the Northeast region are smaller than the homes overall in the United States. The slope of the regression equation, y=124.08x+90127, can be used to help identify how
much the price increases for every 100 square feet. Using the slope and value of x, it can be determined how the price increases as the square feet increase by multiplying the slope and the
Median Housing Price Prediction Model for D.M. Pan National Real Estate Company
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square feet. If the square feet (x) go up by 100 units, this means that the listing price (y) should also increase. To find the price increase for every 100 square feet, the slope 124.08 is multiplied by 100 (square feet). This indicates that the listing price should increase by $12,408 for every 100 square feet.
The graph would be best used for a square footage range of 1145 and 4354. Any square footage value within the spread of data can be used to get a listing price. Caution should be used in predicting a listing price with a square footage value outside the range of data that was used in
creating the regression model.