October 26, 2025
Our regression model is: \(\widehat{y} = b_0 + b_1 \cdot x\) where \(y\) = monthly rent, \(x\) = number of bedrooms
Estimate Std. Error t value Pr(>|t|) (Intercept) 1135.5384 4.893977 232.0277 0 beds 513.8209 2.264135 226.9391 0
Fitted Model: \(\widehat{y} = 1135.54 + 513.82 \cdot x\)
Interpretation: Each additional bedroom increases monthly rent by approx. \(514\) dollars
Analysis: This plot shows that rent prices in the Bay Area have nearly doubled from 2000 to 2018.
Analysis: This plot shows that San Francisco county is the most expensive on average, with the highest median overall.
Analysis: This plot shows that the size, number of bedrooms, and price appear to be correlated.
The linear correlation coefficient measures the strength of the linear relationship between two variables:
\[r = \frac{\sum x_i y_i - \frac{(\sum x_i)(\sum y_i)}{n}}{\sqrt{\left(\sum x_i^2 - \frac{(\sum x_i)^2}{n}\right)\left(\sum y_i^2 - \frac{(\sum y_i)^2}{n}\right)}}\] when \(x\) = number of bedrooms and \(y\) = monthly rent price:[1] 0.4586301
Interpretation: \(0.4586\) suggests a moderate positive correlation between the number of bedrooms and the monthly price of rent. While the number of bedrooms does influence the rent price, other factors such as location, square footage, and amenities also play a significant role.
Analysis: This plot shows that listings with 2 bedrooms are most common, followed by those with 1 bedroom.
sqft_data <- rent_clean %>%
filter(!is.na(sqft), sqft > 200, sqft < 3000) %>%
mutate(price_per_sqft = price / sqft)
ggplot(sqft_data, aes(x = sqft, y = price_per_sqft)) +
geom_point(alpha = 0.2, color = "#8C1D40") +
geom_smooth(method = "lm", color = "#FFC627", linewidth = 1.2) +
labs(x = "Square Feet", y = "Price per Square Foot ($)",
title = "Price Per Square Foot") +
theme_minimal()
This code creates a plot using ggplot that shows the price per square foot.
Analysis: This plot shows that the higher the square feet, the lower the price per square foot.