Project 2

Thesis

My thesis for this project is the sale price of a home is heavily dependent on year of construction, number of full baths, quality of kitchen, size of garage, and size of above ground living area.

Model

## 
## Call:
## lm(formula = gr_liv_area + garage_area + excellent_kitchen + 
##     full_bath + year_built ~ sale_price, data = t_train)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1153.30  -249.44   -21.34   179.04  1827.19 
## 
## Coefficients:
##                 Estimate   Std. Error t value            Pr(>|t|)    
## (Intercept) 2812.3686101   36.8823559   76.25 <0.0000000000000002 ***
## sale_price     0.0062081    0.0001808   34.33 <0.0000000000000002 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 379.4 on 603 degrees of freedom
## Multiple R-squared:  0.6615, Adjusted R-squared:  0.6609 
## F-statistic:  1178 on 1 and 603 DF,  p-value: < 0.00000000000000022

Analysis

• In the model, both the adjusted R squared and p-value are statistically significant.
• The p-value is under 0.05, confirming that it is statistically significant and the model can be used to accurately predict outcomes.
• In the initial regression, the adjusted R squared was 0.6712, meaning we can account for approximately 67.12% of the regression results.
• When creating the line of best fit for the dot plot (using the data from the initial regression), we can use the estimate for both the intercept and the slope along the x axis. In this scenario, the equation for the line would be y = 0.0066x + 2754.61.
• The standard error of the initial regression was 41.16, meaning the average predicted data point was off from the actual result by 41.16 units.

Graphs

This histogram shows the distribution of sales prices in the data. As you can see, the distribution is normal. A log scale was used to better illustrate this distribution. Based on this graph, we can expect other normally distributed variables to correlate heavily with sale price.

This plot shows the different variables correlate to one another. In this graphic, the strongest correlations can be found between sale price:garage area, sales price:above ground living area, and sales price: year built. Based on this graph, we can see that all of the continuous variables used in the analysis are independently correlated to sales price.

This graph shows the most important variables used in the analysis. As is shown in the graph, the two strongest predictors of sale price are above ground living area and garage area. This means that homes with larger above ground living areas or homes with bigger garages tend to have higher selling prices. Additionally, homes with excellent kitchen also tend to have higher selling prices. This variable was created using the ‘Kitchen Quality’ field and filtering for homes that were given an ‘excellent’ grade. Based on this graph, we know that all variables, both discrete and continuous, are strongly correlated to sales price.

Finally, this graph is a dot plot of the regression results. As you can see, the results are tightly correlated with few outliers. This graph proves what was shown on the previous graphs. The data is normally distributed and highly correlated along the line of best fit. This graph proves the thesis that sale price of a home is heavily dependent on year of construction, number of full baths, quality of kitchen, size of garage, and size of above ground living area are all correlated to sale price and are drivers in how expensive a home is.