Linear regression analysis of numerical data with hypothesis testing

Regression Analysis: Real Estatee Sales Prices and Distance to City

This regression analysis seeks to answer the question of how the sales price of Real Estate listed houses changes with the distance from the city. Does the sales price increase or decrease as the distance from the city increases or is there a relationship between the variables at all? Given the attraction of city living and the general trends of suburban house prices, it appears reasonable to hypothesize that the sales price of the houses will decrease as the location of the house moves further away from the city.

Raw Data from Real Estate Listings:

Key: Distance is measured in miles and Sales Price in thousands of dollars.

The regression line, which best illustrates the relationship between the two variables of the data set, takes the equation ? = b + ax. This equation is based on the least squares formula ? (Y -- ?)2, which calculates the minimal possible error of the total data points from a common line. In other words, the regression line produces the most accurate representation of the total data set by minimizing the sum total distance of each data point from the given line. The two variables "a" and "b" were determined using the individual data points, the standard deviation of the mean sales prices and the distance from the city as well as the correlation between the two. The calculations produced the following regression line equation:

= -3.354x + 270.17

Mapping the data on a linear regression graph confirmed the calculations.

The graph shows a negative correlation between the sales prices of houses and the distance from the city. The negative slope of the linear regression line verifies this relationship between the two variables. However, the graph also demonstrates that this correlation is extremely weak. The coefficient of determination (R2), which measures the "fit" of the model, was calculated at 0.12043. This means that the regression line explains only about 12% of the variation in the model.