Project 2 - Sales Price Prediction

Creating tibble, loading data

t_raw <- read.csv("ames.csv")

t <- t_raw %>% 
  clean_names() %>% 
  filter(complete.cases(.)) %>% 
  mutate(at_least_2_stories = ifelse(house_style == "One_Story" | house_style == "One_and_Half_Fin" | house_style == "One_and_Half_Unf", 0, 1))

t_train <- t %>% 
  filter(year_sold <= 2009)
t_test <- t %>% 
  filter(year_sold == 2010)

Histogram and Tables of Variables Used

## 
##    0    1 
## 1814 1116

Correlation and Pairs

Making Model

## 
## Call:
## lm(formula = sale_price ~ gr_liv_area + full_bath + garage_area + 
##     bedroom_abv_gr + at_least_2_stories, data = t_train)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -523983  -21213     -74   20500  272704 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         15608.706   3907.713   3.994 6.67e-05 ***
## gr_liv_area            95.888      2.833  33.847  < 2e-16 ***
## full_bath           20662.191   2179.553   9.480  < 2e-16 ***
## garage_area           114.236      5.096  22.415  < 2e-16 ***
## bedroom_abv_gr     -20950.145   1341.886 -15.612  < 2e-16 ***
## at_least_2_stories -13086.688   2085.276  -6.276 4.07e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 46780 on 2583 degrees of freedom
## Multiple R-squared:  0.6629, Adjusted R-squared:  0.6623 
## F-statistic:  1016 on 5 and 2583 DF,  p-value: < 2.2e-16

Testing Data

## [1] "Mean t_test$residual" "1685.7602688377"

## [1] "Rsme of test"     "43206.7101451084"

## [1] "Rsme of train"    "46730.0378130818"

ggplot() +
  geom_point(data = t_train, mapping = aes(predicted, sale_price), alpha = 0.2, color = "blue") +
  geom_point(data = t_test, mapping = aes(predicted, sale_price), alpha = 0.2, color = "green") +
  geom_abline(intercept = 0, slope = 1) +
  scale_x_continuous(labels = scales::label_dollar()) +
  scale_y_continuous(labels = scales::label_dollar())

hist(t_train$residual)

hist(t_test$residual)

R-squared

## [1] "r-squared for train" "0.662932032477308"

## [1] "r-squared for test" "0.663849068321803"

Analysis

Thesis

In this project, several key factors were identified that impact the sale price of homes. Living area, number of full bathrooms, garage area, number of bedrooms, and the number of stories to the house play crucial roles in determining house value.

Variables

After running the ggcorplot, all the variables used were shown to have a relationship with the sale price of the home. The extremely low p-values of the variables from the model summary also show significance.

1. Living Area (gr_liv_area):

   • For every additional square foot of living area, the predicted sale price increases by approximately $95.88.

   • Larger living areas tend to correlate with higher prices.

2. Number of Full Bathrooms (full_bath):

   • Each additional full bathroom adds approximately $20662.19 to the predicted sale price.

   • Houses with more bathrooms tend to be more valuable.

3. Garage Area (garage_area:

   • For every additional square foot of garage area, the predicted sale price increases by approximately $114.24.

   • Larger garages contribute positively to the house price.

4. Bedrooms Above Ground (bedroom_abv_gr):

   • Each additional bedroom above ground reduces the predicted sale price by approximately $20950.15.

   • More bedrooms may decrease the overall value.

5. At Least 2 Stories (at_least_2_stories):

   • Houses with at least 2 stories have a predicted sale price approximately $13086.69 lower than single-story houses.

   • Single-story homes tend to be more valuable.

Predicted Values/Residuals

1. Mean Residual:
   • On average the model tends to overestimate the sale price by $1685.76
2. RMSE
   • Test rmse was 43206.71, which shows the average absolute difference between the predicted and actual sales price. A lower number would be preferable.
3. Histogram of Residuals
   • The histograms of both t_train$residuals and t_test$residuals were on a normal bell curve. This implies that the errors are random and unbiased.
4. R-squared values
   • The r-squared value for train is 0.6629, meaning that around 66.29% of the variability in sales price can be explained by the model.
   • The r-squared value for test is 0.6638, suggesting that the model generalizes well for unseen data