Introduction
The use of statistical predictive models makes it possible to predict organizational changes, including sales. Although sales dynamics for companies are a difficult variable to accurately predict, underlying trends can be determined using simple linear regression equations. This paper uses regression analysis precisely to determine the effect of square footage, that is, floor space, on its listing price. At first glance, it would seem that an increase in square footage naturally leads to an increase in the price of space — but this assumption can be evaluated with statistics. To be specific, East South Central is used as the selected region, with a sample size of 30 out of 100 lines.
Regression Equation
For this sample, a scatter plot was constructed in which the independent variable was the floor area, and the dependent factor was the listing price. For this data, the linear regression equation was equal:
It follows from this equation that, indeed, when the area of the room increases, there is an increase in the listing cost for commercial real estate.
Determine r
A correlation analysis was also run to evaluate this relationship. The result of the correlation analysis is the Pearson coefficient, which explains the direction and strength of the relationship between the variables. Thus, the calculations showed that Pearson’s correlation coefficient is 0.964 — from this, it follows that there is a positive relationship between the variables. In addition, Pearson’s correlation coefficient shows that the strength of the relationship between the variables is strong. A correlation value of 0.964 reports a strong positive relationship. It follows that it can be postulated that when commercial space in the East South Central region increases, there is indeed an increase in the listing price.
Examine the Slope and Intercept
The slope and y-intercept can also be inferred from the regression equation. Thus, the slope of 104.15 shows that there is a 104.15 increase in the listing price for every square foot of floor space. Meanwhile, the physical meaning of the y-intercept is missing-it shows that with zero floor space, the listing price is 32.425. If one imagines that zero areas imply that there is no room at all, including no area of territory, then the y-intercept makes no sense in this case. The x-intercept also makes no sense. Solving the equation with respect to zero shows that the x-intercept is -311.33: that is, for a zero budget, you can buy space of -311.33 square feet, which also makes no sense in the context of this problem.
R-squared Coefficient
The coefficient of determination for this regression analysis shows that R2 is 0.9294. In general, this data shows that this regression model explains up to 92.94 percent of the listing price variance for this sample (Bloomenthal, 2021). One could interpret this finding differently-the linear regression model was entirely accurate for this distribution.
Conclusions
In this paper, a regression analysis was conducted to determine the nature of the relationship between listing price and commercial space in East South Central. If one performs regression analysis for the entire population (MAT 240 Real Estate Data), one finds that there is also an increase in listing price with an increase in square footage. The difference between the sample results and the population results is in the values of the coefficients of determination — the linear relationship was more accurate for the sample, as opposed to the population (R2 = 0.6789). From the regression equation constructed, one can infer a slope. That is, it is easier to calculate an increase in price for an increase in area. In addition, the regression equation can be used to predict the listing price for a particular area, which will be helpful for realtors.
Reference
Bloomenthal, A. (2021). Coefficient of determination. Investopedia. Web.