#MODEL
library(ggcorrplot)
##For the following variables, they all impact sale price.
## -year_built has a positive coefficient which makes sense, showing that as the year increases(gets newer), the sale price also tends to increase by $449
## -lot_area also has a positive coefficient showing an increase of 95 cents in sale price for every unit increase in area
## -gr_liv_area has a positive coefficient and the sale price increases by around $55 for every unit increase in area
## -total_bsmt_sf has a positive coefficient and as the square footage increase by a unit, the sale price increases by about $33
## -overall_qual_level is a categorical set of data which has a positive correlation also, as the quality level increases by 1 level then the sale price increases by around $20000
model <- lm(sale_price ~ year_built + lot_area + gr_liv_area + total_bsmt_sf + overall_qual_level, data = t_train)
summary(model)
##
## Call:
## lm(formula = sale_price ~ year_built + lot_area + gr_liv_area +
## total_bsmt_sf + overall_qual_level, data = t_train)
##
## Residuals:
## Min 1Q Median 3Q Max
## -182916 -18111 -1378 15219 256017
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -9.533e+05 4.723e+04 -20.18 <2e-16 ***
## year_built 4.449e+02 2.492e+01 17.86 <2e-16 ***
## lot_area 9.481e-01 7.930e-02 11.96 <2e-16 ***
## gr_liv_area 5.562e+01 1.538e+00 36.17 <2e-16 ***
## total_bsmt_sf 3.877e+01 1.737e+00 22.32 <2e-16 ***
## overall_qual_level 2.011e+04 6.653e+02 30.23 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 31490 on 2889 degrees of freedom
## (35 observations deleted due to missingness)
## Multiple R-squared: 0.818, Adjusted R-squared: 0.8177
## F-statistic: 2598 on 5 and 2889 DF, p-value: < 2.2e-16
t_train <- t_train %>%
mutate(predict = predict(model, newdata = t_new),
residuals = sale_price - predict)
error <- sqrt(mean(t_train$residuals ^2 ))
t_numeric <- t_train %>%
select(where(is.numeric)) %>%
select(sale_price, year_built, lot_area, first_flr_sf, gr_liv_area, total_bsmt_sf, overall_qual_level)
pairs(t_numeric)
##the errors represent the distance between the actual sale price and the predicted sale price, the residuals range from -182916 to 256017 with a median of -1378. This means that there are some outliers in the data but the model tends to over/underestimate the sale price by 1378.
#PREDICTIONS
hist(model$residuals)
predictions <- predict(model, newdata = t_test)
rmse <- sqrt(mean((t_test$sale_price - predictions)^ 2))
r_squared <- cor(t_test$sale_price, predictions)^2
##My R squared value for the test data set is 0.81421 which is relatively high, this means that roughly 81% of the dependent variable (sale price) is dependent upon the independent variable I chose.
##My rmse value is 32222 which means that the predicted sale price is off by roughly that much compared to the actual value. Lower rmse values mean that a model is more accurate, but compared to the price that homes are sold for, this value is not too terribly bad. Even though it could be much better, once I got to this point everything I tried changing made this value worse.
#GRAPHS
ggplot(t_test, aes(x = total_area, y = sale_price, color = overall_qual_level)) +
geom_point(alpha = 0.5) +
scale_color_gradient(low = "blue", high = "red") +
labs(title = "Relationship between Total Area, Overall Quality, and Sale Price",
x = "Total Area",
y = "Sale Price",
color = "Overall Quality") +
theme_minimal()
ggplot(t_test, aes(x = overall_qual_level, y = sale_price, fill = factor(overall_qual_level))) +
geom_boxplot() +
labs(title = "Distribution of Sale Price by Overall Quality",
x = "Overall Quality",
y = "Sale Price") +
scale_fill_brewer(palette = "Set3") +
theme_minimal()
