Median Housing Price Prediction Model for D.M. Pan Real Estate Company

Module Two Notes

[Copy and paste any relevant information from your Module Two assignment here to assist you in completing this assignment. This section is not graded and is only provided to help you easily review Module Two assignment information while completing this assignment.]

Regression Equation

[Insert the regression equation for the line of best fit using the scatterplot from your Module Two assignment.]

Determine r

[Determine r and what it means, including determining the strength of the correlation and discussing how you determine the direction of the association between the two variables.]

Examine the Slope and Intercepts

[Draw conclusions from the slope and intercept in the context of this problem and determine the value of only the land.]

R-squared Coefficient

[Explain what R-squared means in the context of this analysis.]

Conclusions

[Reflect on the relationship between square feet and sales price by addressing key considerations such as the comparison between your selected region and overall homes in the United States, as well as analyzing how the slope can help identify price changes, how the regression equation can help identify appropriate listing prices, and which graph would be best suited to informing square footage ranges.]

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Module Two Notes

This report focuses on a random sample selected from the East North Central. The median listing price had a mean of $206,053; a median of $216,684 and standard deviation of 74599.04556. The median square feet had a mean of 1763, a median of 1733 and standard deviation of 237.5108072.

Regression Equation

The regression coefficients y= mx+b as calculated on the data excel sheets are:

Y = 230.422651(x) + -200275.063

Determine r

R is known as a coefficient of linear correlation. R values are used to measure the direction and strength of the variables and usually range between -1 and +1. A positive value usually shows positive linear correlation between variables while a negative value shows a negative linear correlation between the variables. In case there is very little or no correlation, the value of r is close to 0.

In our sample on East North Central, the value of r is 0.73362695 as calculated in Microsoft excel. This value, 0.73362695, is closer to 1 and since it’s a positive value, it indicates a strong linear correlation between the X and Y variables and therefore, an increase in X value will lead to an increase in Y value as well.

Slope and Intercepts

The slope value is 230.42 and the intercept value is -200275. The slope value indicates that the for every square foot increased the price listing increases by $230.42 while the intercept value indicates that if 0 square foot was for sale, the price would be $-200,27. The expectation would be that the price would also be zero.

To solve for the price of 1200 square feet according to the regression equation;

Y = 230.422651(x) + -200275.063

Y= 230.422651(1200) + -200275.063

Y= $76,232.11877

The price of the property should therefore be $76,232.11

R-squared Coefficient

R- Squared gives the proportion by which the variation of one variable fluctuates in relation to the other variable. This means R squared shows the proportion/ percentage by which Y changes/fluctuates when the value of X changes. The values of R-squared lie between 0 and 1. The closer the value is to 0 shows that the influence one variable has over the other is very little while the closer the value is to 1 shows that there influence one variable has over the other is very strong. 

The value of R in the sample is 0.73362695. R squared is therefore 0.5382085. The value has also been calculated in excel. In percentage the value of r squared is 53.8%. This means that 53.8% of the value of Y can be explained by the value of X. the other 46.2% are not influenced by the value of X.

Conclusions

According to the sample size at East North Central, as the price per square foot increases, there is an increase in the price of the house. The price of a house may also depend on other things other than the square feet of the house. For example, the location of the house. Houses located in cities are more expensive compared to houses located in the country side. If we consider the general area of the East North Central region, the sample is a good prediction of the price of homes through the United States. This is because the sample was picked out on random. However in case the East North Central region is on the country side, it may not predict the prices per square feet accurately for areas in the city.

The slope can help by approximating the price change in houses. 230.422651(x) is the slope. So if another house is 100 square feet more; using the slope to approximate the increase in price; the price of the house will increase by 230.422651(100) which is 23,042.2651. The regression equation can be used to find listings of houses between the price of $50,000 and $400,000. This is because the sample size used had that range of prices.