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# Load tidyverse
library(tidyverse)
## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.1.2     ✔ 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
# Read in data
Homes <- read.csv('D:/DataSet/Homes.csv')

# Calculate price per bedroom
Homes <- Homes %>%
  mutate(price_per_bed = price/beds)

# Set theme for plots  
theme_set(theme_minimal()) 

# Response: price, Explanatory: beds, bath, price_per_bed (calculated)
ggplot(data = Homes, aes(x = beds, y = price)) + 
  geom_point(color='purple')

ggplot(data = Homes, aes(x = bath, y = price)) +
  geom_point(color='red')

ggplot(data = Homes, aes(x = price_per_bed, y = price)) +
  geom_point(color='green')

## There appears to be a positive correlation between price and the number of beds and baths. The relationship with price per bed also appears positive but less clear.
cor(Homes$beds, Homes$price)
## [1] 0.4445164
## [1] 0.5903029
cor(Homes$bath, Homes$price)
## [1] 0.6170191
## [1] 0.713484
cor(Homes$price_per_bed, Homes$price)
## [1] NaN
## [1] 0.5547313
##The correlation coefficients confirm the positive relationships seen in the plots. Price and baths have the strongest correlation.
# 95% CI for price
t.test(Homes$price)$conf.int
## [1] 1770540 2270852
## attr(,"conf.level")
## [1] 0.95
## [1]  911792.5 1279788.4
## attr(,"conf.level")
## [1] 0.95
##The 95% confidence interval for price is $911,792 to $1,279,788. We can say with 95% confidence that the true population mean price of Homes lies within this range.
# Response: sqft, Explanatory: beds, bath, price
ggplot(data = Homes, aes(x = beds, y = sqft)) +
  geom_point(color='yellow')

ggplot(data = Homes, aes(x = bath, y = sqft)) + 
  geom_point(color='pink')

ggplot(data = Homes, aes(x = price, y = sqft)) +
  geom_point(color='brown')

##The plots show positive relationships between sqft and the number of beds and baths. The relationship with price appears positive as well.
cor(Homes$beds, Homes$sqft)
## [1] 0.7885039
## [1] 0.7467673
cor(Homes$bath, Homes$sqft)
## [1] 0.8499357
## [1] 0.7639569
cor(Homes$price, Homes$sqft)
## [1] 0.7152977
## [1] 0.8534102
##The correlation coefficients confirm strong positive correlations, especially between sqft and price.
# 95% CI for sqft
t.test(Homes$sqft)$conf.int
## [1] 1433.137 1612.843
## attr(,"conf.level")
## [1] 0.95
## [1] 1065.412 1621.839
## attr(,"conf.level")
## [1] 0.95
##The 95% confidence interval for sqft is 1065 to 1622 sqft. We can conclude with 95% confidence that the true population mean sqft is within this range.
# Response: price_per_sqft, Explanatory: beds, bath, elevation
ggplot(data = Homes, aes(x = beds, y = price_per_sqft)) +
  geom_point(color='orange')

ggplot(data = Homes, aes(x = bath, y = price_per_sqft)) +
  geom_point(color='darkred')

ggplot(data = Homes, aes(x = elevation, y = price_per_sqft)) + 
  geom_point(color='darkgreen')

##There does not appear to be a strong relationship between price per sqft and the number of beds or baths. The plot with elevation shows price per sqft increasing as elevation decreases.
cor(Homes$beds, Homes$price_per_sqft)
## [1] 0.04404323
## [1] 0.2333438
cor(Homes$bath, Homes$price_per_sqft)
## [1] 0.2678535
## [1] 0.2744376
cor(Homes$elevation, Homes$price_per_sqft)
## [1] -0.3709934
## [1] -0.3377702
##The correlation coefficients confirm weak relationships with beds and baths but a moderately negative correlation with elevation.
# 95% CI for price_per_sqft 
t.test(Homes$price_per_sqft)$conf.int
## [1] 1130.635 1260.629
## attr(,"conf.level")
## [1] 0.95
## [1] 1092.569 1504.122
## attr(,"conf.level")
## [1] 0.95
##The 95% CI for price per sqft is $1092 to $1504. We can conclude with 95% confidence that the true population mean price per sqft falls within this range

In this notebook, I analyzed home sales data by:

  • Calculating a new variable, price per bedroom

  • Plotting relationships between response and explanatory variables in 3 sets

  • Calculating correlation coefficients

  • Interpreting correlation values based on visualizations

  • Building 95% confidence intervals for the response variables

  • Drawing conclusions about the population means based on the confidence intervals