D.M. Pan Real Estate Company's Median Housing Price Prediction Model for 2021

Module Two Notes 

The simple random sample of 30 for the East North Central region is indicated below. 

There are two key variables, namely the x-variable and y-variable. The x-variable is regarded as the independent variable, and it represents the square feet of the specific house. The y-variable is the dependent sample given that it is affected by the x-variable. The house listing price is dependent on the size of the house, which is measured in square feet. 

Regression Equation 

The regression equation is showcased in the scatterplot below. 

Determine R 

The sample's r-value or the coefficient of correlation is 0.91. The metric has been computed in Excel through the CORREL function. The assessment of the r-value can show the direction and the strength of the tendency of the house size and listing price variables to vary together. The computed correlation coefficient is between -1 and 1, as expected. The strength of the relationship between two distinct variables is assessed by examining the correlation coefficient's absolute value. Essentially, a strong correlation is said to exist when the correlation coefficient value is above 0.7 (Keller, 2017). The computed correlation coefficient value of 0.91 is above 0.7, and, as a result, the relationship between the house size and listing price variables is strong. The correlation coefficient sign illustrates the direction of the relationship between variables. A positive relationship is obtained when the correlation coefficient’s absolute value has a positive sign. If the absolute value is negative, it means that the relationship between the key variables is negative. The absolute value of 0.91 is positive, and, as a consequence, there is a positive relationship between the square footage of the house and its listing price. A correlation coefficient of +1 depicts a perfect positive relationship (Keller, 2017). The computed correlation coefficient of 0.91 is near +1, meaning that the positive relationship between the house size and listing price is almost perfect. 

Examine the Slope and Intercepts 

The slope and y-intercept can be derived from the regression equation. The slope is 91.588, while the y-intercept is 63,029. The slope of the trendline depicts how much the value of y shifts for every change in the value of x. The slope of 91.588 means that for every one unit that the independent variable increases, the dependent variable increases by 91.588 units. In this respect, for every unit increase in the house's square footage, the house's listing price goes up by 91.588 units. The y-intercept represents the actual point at which the trendline crosses the vertical y-axis (Keller, 2017). It also depicts the starting value. In this regard, the starting listing price is $63,029. This intercept makes sense based on the observation of the trendline. When the trendline is extrapolated, it is likely to intercept the y-axis at a specific point between $50,000 and $100,000. 

The value of the land is the y-intercept which is $63,029. This value which is high, makes sense given the valuable nature of land. The final listing price of a house should include the cost of purchasing the land and constructing the house. 

R -squared Coefficient

The r-squared value is 0.8282. This value has been computed in excel through the RSQ function. It can also be calculated by finding the square value of the correlation coefficient. The r-squared value illustrates how well the specific regression equation fits the observed data (Keller, 2017). It also shows the proportion of the variance in the y-variable that the regression model and x-variable predict. The coefficient of determination is 0.8282, meaning that around 83% of the data fits the regression equation. In addition, 83% of the variation in the listing price has been explained just by using the house's square footage in predicting outcomes. The coefficient value of 0.8282 is high, meaning that the regression equation is a good fit for the sample data. 

Conclusions 

The trendline, regression equation, and slope provide sufficient evidence of the positive relationship between the house size and listing price variables. The coefficient correlation value depicts the strength of the positive relationship between the two distinct variables. The square footage for houses in the East North Central region is different than for homes overall in the US. The descriptive statistics of the sample and the population reveals the differences between the East North Central region and the whole of the US. The mean and median square footage for the East North Central region sample are 1920 and 1747, respectively. The mean and median square footages for the population are 1944 and 1901, respectively. The standard deviation of square footage for the East North Central region and the entire US are different, meaning that the square footage for homes in the two areas are different. 

For every 100 square feet, the house’s listing price increases by $9,158.80. The slope derived from the regression equation can be used to compute the changes in the house listing price. The changes in listing price can be determined by multiplying the changes in the square footage by the slope. 

The graph would be best used for a square footage range of 5,000. Based on the graph, the data points lie between 1,000 and 6,000 square feet. The difference between the highest and lowest square footage is 5000. 

Reference 

Keller, G. (2017).  Statistics for management and economics . Mason, OH: Cengage.