MAT 240 Module Three Assignment Jackie
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Jan 9, 2024
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Housing Price Prediction Model for D.M. Pan Real Estate Company
Jackie Sechrist
September 13,2023
MAT-240 Applied Statistics Southern New Hampshire University
Instructor Wasim Barham
Module Two Notes
The listing price is the Y axis. Square foot area is the X axis. The shape is linear because the trend line is positive, even though the plot is kind of clustered up in one spot, the association between x
and y
in the scatterplot is a positive one, you can see from data point to data point that the selling price is higher as the square footage increases. The correlation is positive, not perfectly linear but the association between the two is a positive one.
1,000 2,000 3,000 4,000 5,000 6,000 7,000 - 100,000 200,000 300,000 400,000 500,000 600,000 700,000 800,000 f(x) = 112.77 x + 38972.08
Listing Price and Square foot area Square foot area
Listing Price
Regression Equation
Regression Equation Y= 112.77x + 38972
Y^=38972.08+112.77x
Determine r
0.94
According to the scatterplot and my random sample, the “r” also known as the correlation coefficient is a 0.94 which is a positive, strong correlation, shows a close association between the two variables. This correlation is strong because it is close to 1. I determined the direction of the association directly from the best fit line, it was going up, which means that’s a positive correlation, and with the “r” close to one, it determines a variation that is considered good. For the value of R anything less than 0.40 is considered weak, 0.40<0.80 is moderate and 0.80 and greater is considered strong strength in correlation. There are a few outliners, but again we are going to dismiss them with the fact that when taking on a sample in a size of only 30 and that the average for listing price is substantially lower than the
outlines presented, chances are these are just showing up because of sample size or the lake off data for homes in that range. Examine the Slope and Intercepts
Slope- 112.76
Intercept- 38972.08- It represents the point where this line crosses the y-axis.
You would expect listing price to go up, based on square root area when looking at the slope and the intercepts. Based on the regression equation my slope is 112.76 and the y intercept is 38,972 if we were to change x to 0, then the square foot area is 0, then you would be subtracted the answer, which if X is 0 then its), then the sum is now -38,972 which makes zero cents.. One reason is because houses don’t go on the market and sell if the square foot was zero, and this conclusion means that by chance it was sold as only the land it would be a negative number. This doesn’t make sense to be the value because the land doesn’t have a value when negative or land only. R
-squared Coefficient
0.88
The R-squared coefficient- also known as the coefficient of determination. This is the proportion of the listing price that is explained by the square foot area. In the context of this analysis R-squared is the proportion of Y that is explained by X, so in this case, “how much does the listing price vary based on
the square foot average of the house.” In other words, r-squared shows how well the data fit the regression model. Conclusions
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If you look at the slope and the direction the regression line is headed, you could use this graph to determine the price of house and the amount of square footage you would expect for it to have, in the West South-Central Region. If you reflect on the relationship between the National homes and my region you will see that the region, I have selected is lower than the National level in all requested statistics. (median, stdev.s,min, the quartiles, and the max) for listing price. This data shows that the square foot area is different at a national level, and the price per square foot is different. Reflecting on the relationship between square feet and sales price you would conclude for each unit change in square footage-- so if the square footage changes by 1, the price goes up by $112.72
So if we go back to the slope here-- remember, that the slope is plus 112.72 so if the square feet go up 100 square feet that the listing price will also go up, the price would be $11,276 if the square foot was 100, and $112,765 if the square foot increased 1.000 , basically per until times 100. So, if you question how your regression equation or the scatter plot could help guide your decision making, you could use it to help with a selection and your home buying situations by just plugging in the square footage of the
house back into the data to get a predicted listing price. Intercept + slope times by square foot average, be mindful when using predicted prices, when outside the range of your graph so let’s say 1200 on the low side which gives me $174,000 listing price, this does not add up, when the data shows otherwise.
1,400 2,400 3,400 4,400 5,400 ($200,000)
($100,000)
$0 $100,000 $200,000 $300,000 $400,000 $500,000 $600,000 $700,000 $800,000 Residual Chart
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Median Housing Price Prediction Model for D.M. Pan National Real Estate Company
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