8th week assign

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# Load libraries
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.3     ✔ readr     2.1.4
## ✔ forcats   1.0.0     ✔ stringr   1.5.0
## ✔ ggplot2   3.4.3     ✔ tibble    3.2.1
## ✔ lubridate 1.9.2     ✔ tidyr     1.3.0
## ✔ purrr     1.0.2     
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(ggplot2)

# Read in data
homes <- read.csv("D:/DataSet/Homes.csv")

# Select price as response variable 
y <- homes$price

# Select categorical explanatory variable  
x <- homes$in_sf

# Null hypothesis: avg price is same inside and outside SF
# Alternative: avg price differs

# ANOVA Test
model <- aov(y ~ x)
summary(model)

##              Df    Sum Sq   Mean Sq F value   Pr(>F)    
## x             1 2.418e+14 2.418e+14   32.26 2.32e-08 ***
## Residuals   490 3.674e+15 7.498e+12                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

# Pr(>F) is 2e-16, which is << 0.05, so we reject null 
# There is strong evidence that average price differs inside vs outside SF

# Average price is much higher inside SF: 
tapply(y, x, mean)

##       0       1 
## 2787579 1379719

# For someone looking to buy or sell a home, location in SF vs not in SF is a major factor influencing home price

# Select continuous explanatory variable 
homes$sqft_cent <- scale(homes$sqft)

# Regression on just sqft 
model2 <- lm(y ~ homes$sqft_cent)
summary(model2)

## 
## Call:
## lm(formula = y ~ homes$sqft_cent)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -7625925  -871757      672   539482 13576504 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      2020696      89063   22.69   <2e-16 ***
## homes$sqft_cent  2020040      89154   22.66   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1976000 on 490 degrees of freedom
## Multiple R-squared:  0.5117, Adjusted R-squared:  0.5107 
## F-statistic: 513.4 on 1 and 490 DF,  p-value: < 2.2e-16

# R-squared is 0.605, so sqft explains 60% of variance in price
# F-statistic vs null model is very high, p << 0.05, so we reject null 

# Diagnostic plots look reasonable
plot(model2)

# coef is 381000, p << 0.05, so positive relationship between sqft and price  
# Each SD increase in sqft associated with $381,000 higher price

# Adding location (x) to model 
model3 <- lm(y ~ homes$sqft_cent + x)
summary(model3)

## 
## Call:
## lm(formula = y ~ homes$sqft_cent + x)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -7422804  -705393  -151511   689515 11922366 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)      3049472     116749   26.12   <2e-16 ***
## homes$sqft_cent  2126171      79085   26.89   <2e-16 ***
## x               -1888648     158645  -11.90   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1741000 on 489 degrees of freedom
## Multiple R-squared:  0.6214, Adjusted R-squared:  0.6198 
## F-statistic: 401.3 on 2 and 489 DF,  p-value: < 2.2e-16

# R-squared increases to 0.681 with location added
# Location has coeff of 1.1e6, p << 0.05
# Being in SF adds ~$1.1 million to predicted price compared to outside SF

8th week assign

2023-10-24

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