Project 1 Meeting

```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)

Summary

Dataset Description: The dataset used for this project is the Ames Housing dataset, which contains detailed information on 2930 homes in Ames, Iowa. The dataset has 82 columns representing various aspects such as lot size, building features, and sale prices.

The dataset can be found on github with detailed documentation available on below link

https://github.com/leontoddjohnson/datasets/blob/main/data/ames.csv

https://jse.amstat.org/v19n3/decock/DataDocumentation.txt

Main Question/Goal:

The primary goal of this project is to analyze the relationships between key numeric variables, such as Sale Price, Lot Area, and Above Ground Living Area. This includes understanding the influence of house features on sale prices and identifying patterns, such as the impact of price per square foot on overall value.

Visualizations:

• SalePrice vs Lot Area:

  # Load necessary libraries
  library(ggplot2)
  library(dplyr)

  ## 
  ## Attaching package: 'dplyr'

  ## The following objects are masked from 'package:stats':
  ## 
  ##     filter, lag

  ## The following objects are masked from 'package:base':
  ## 
  ##     intersect, setdiff, setequal, union

  # Load the dataset
  ames <- read.csv('D:/Stats for DS/ames.csv', header = TRUE)
  
  # Selecting relevant columns for analysis
  variables <- ames %>%
    select(SalePrice, Lot.Area, Gr.Liv.Area) %>%
    na.omit()
  
  # Plot 1: SalePrice vs Lot Area
  ggplot(variables, aes(x = Lot.Area, y = SalePrice)) +
    geom_point(color = "blue", alpha = 0.6) +
    labs(title = "Sale Price vs Lot Area", 
         x = "Lot Area (sq ft)", 
         y = "Sale Price ($)") +
    theme_minimal()

  

1. A scatter plot shows a weak positive relationship between sale price and lot area, with some outliers.

2. This relationship is worth further investigation to understand if certain lot sizes lead to disproportionately high sale prices.

• SalePrice vs Above Ground Living Area:

  ggplot(variables, aes(x = Gr.Liv.Area, y = SalePrice)) +
    geom_point(color = "green", alpha = 0.6) +
    labs(title = "Sale Price vs Above Ground Living Area", 
         x = "Above Ground Living Area (sq ft)", 
         y = "Sale Price ($)") +
    theme_minimal()

  

  1. A much stronger positive correlation is evident between the sale price and the above-ground living area.

  2. Investigating this further will help determine if larger homes provide better value for buyers, and if there are diminishing returns as living area increases.

# Calculate the correlation matrix
correlation_matrix <- cor(variables)

# Print the correlation matrix
print(correlation_matrix)

##             SalePrice  Lot.Area Gr.Liv.Area
## SalePrice   1.0000000 0.2665492   0.7067799
## Lot.Area    0.2665492 1.0000000   0.2855992
## Gr.Liv.Area 0.7067799 0.2855992   1.0000000

Plan Moving Forward:

• Investigate Price per Square Foot and its relationship with Lot Area and Living Area.

• Identify outliers in the data and see how they impact relationships.

• Explore whether features like Total Basement Area and Garage Area contribute significantly to sale prices.

• Perform Exploratory Data Analysis (EDA).

• Built a Regression model for predicting Sale Price.

Initial Findings

Hypothesis 1:

• Larger homes (greater Above Ground Living Area) tend to have a higher Sale Price.

• Visualization: A scatter plot of SalePrice vs Gr.Liv.Area shows a strong positive relationship, with a correlation coefficient of 0.71.

Hypothesis 2:

• Homes with a larger lot area may not proportionally increase in Sale Price.

• Visualization: The scatter plot of SalePrice vs Lot.Area reveals a weak correlation of 0.27, suggesting other factors influence the price more than just lot size.

To-do List:

• Test both hypotheses by further analyzing subsets of data, such as different home categories or neighborhoods.

• Investigate multivariate relationships by including more features like Garage Area, Basement Area, and Age of the house in the analysis.

• Calculate and visualize residuals from regression models to examine whether non-linear models might be more appropriate.