Group_2_ASSIGNMENT

GROUP MEMBERS

1. Mercy Cheptoo 21/05823

2. Edwin Mucheru 21/06264

3. Celine Salesa 21/08374

4. JoyComfort Wangari 21/05738

library(readxl)
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

library(ggplot2)
library(gridExtra)

## 
## Attaching package: 'gridExtra'

## The following object is masked from 'package:dplyr':
## 
##     combine

library(corrplot)

## corrplot 0.95 loaded

IMPORTING THE DATASET

House_pricing_data <- read_excel("/Users/cheptoo/Downloads/House pricing data.xlsx")
View(House_pricing_data)

checking the columns

colnames(House_pricing_data)

##  [1] "HouseId"                  "MSZoning"                
##  [3] "LotAreaSquareFeet"        "LandSlope"               
##  [5] "BuildingType"             "OverallCondition"        
##  [7] "YearBuilt"                "ExteriorCondition"       
##  [9] "Foundation"               "TotalBasementSquareFeet" 
## [11] "HeatingQualityCondition"  "CentralAirConditioning"  
## [13] "1stFloorSquareFeet"       "2ndFlrSquareFeet"        
## [15] "LivAreaSquareFeet"        "FullBathrooms"           
## [17] "Bedrooms"                 "KitchenQualityCondition" 
## [19] "TotalRooms"               "GarageArea"              
## [21] "TotalPorchAreaSquareFeet" "MonthSold"               
## [23] "YearSold"                 "SaleType"                
## [25] "SaleCondition"            "SalePrice"

EDA

To understand the structure of the data, distribution, identify trends and relationship between the variables

head(House_pricing_data)

## # A tibble: 6 × 26
##   HouseId MSZoning     LotAreaSquareFeet LandSlope BuildingType OverallCondition
##     <dbl> <chr>                    <dbl> <chr>     <chr>                   <dbl>
## 1       1 Residential…              8450 Gentlesl… Single-fami…                5
## 2       2 Residential…              9600 Gentlesl… Single-fami…                8
## 3       3 Residential…             11250 Gentlesl… Single-fami…                5
## 4       4 Residential…              9550 Gentlesl… Single-fami…                5
## 5       5 Residential…             14260 Gentlesl… Single-fami…                5
## 6       6 Residential…             14115 Gentlesl… Single-fami…                5
## # ℹ 20 more variables: YearBuilt <dbl>, ExteriorCondition <chr>,
## #   Foundation <chr>, TotalBasementSquareFeet <dbl>,
## #   HeatingQualityCondition <chr>, CentralAirConditioning <chr>,
## #   `1stFloorSquareFeet` <dbl>, `2ndFlrSquareFeet` <dbl>,
## #   LivAreaSquareFeet <dbl>, FullBathrooms <dbl>, Bedrooms <dbl>,
## #   KitchenQualityCondition <chr>, TotalRooms <dbl>, GarageArea <dbl>,
## #   TotalPorchAreaSquareFeet <dbl>, MonthSold <dbl>, YearSold <dbl>, …

tail(House_pricing_data)

## # A tibble: 6 × 26
##   HouseId MSZoning     LotAreaSquareFeet LandSlope BuildingType OverallCondition
##     <dbl> <chr>                    <dbl> <chr>     <chr>                   <dbl>
## 1    1455 Floating Vi…              7500 Gentlesl… Single-fami…                5
## 2    1456 Residential…              7917 Gentlesl… Single-fami…                5
## 3    1457 Residential…             13175 Gentlesl… Single-fami…                6
## 4    1458 Residential…              9042 Gentlesl… Single-fami…                9
## 5    1459 Residential…              9717 Gentlesl… Single-fami…                6
## 6    1460 Residential…              9937 Gentlesl… Single-fami…                6
## # ℹ 20 more variables: YearBuilt <dbl>, ExteriorCondition <chr>,
## #   Foundation <chr>, TotalBasementSquareFeet <dbl>,
## #   HeatingQualityCondition <chr>, CentralAirConditioning <chr>,
## #   `1stFloorSquareFeet` <dbl>, `2ndFlrSquareFeet` <dbl>,
## #   LivAreaSquareFeet <dbl>, FullBathrooms <dbl>, Bedrooms <dbl>,
## #   KitchenQualityCondition <chr>, TotalRooms <dbl>, GarageArea <dbl>,
## #   TotalPorchAreaSquareFeet <dbl>, MonthSold <dbl>, YearSold <dbl>, …

glimpse(House_pricing_data)

## Rows: 1,460
## Columns: 26
## $ HouseId                  <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14…
## $ MSZoning                 <chr> "Residential Low Density", "Residential Low D…
## $ LotAreaSquareFeet        <dbl> 8450, 9600, 11250, 9550, 14260, 14115, 10084,…
## $ LandSlope                <chr> "Gentleslope", "Gentleslope", "Gentleslope", …
## $ BuildingType             <chr> "Single-family Detached", "Single-family Deta…
## $ OverallCondition         <dbl> 5, 8, 5, 5, 5, 5, 5, 6, 5, 6, 5, 5, 6, 5, 5, …
## $ YearBuilt                <dbl> 2003, 1976, 2001, 1915, 2000, 1993, 2004, 197…
## $ ExteriorCondition        <chr> "Average/Typical", "Average/Typical", "Averag…
## $ Foundation               <chr> "Poured Contrete", "Cinder Block", "Poured Co…
## $ TotalBasementSquareFeet  <dbl> 856, 1262, 920, 756, 1145, 796, 1686, 1107, 9…
## $ HeatingQualityCondition  <chr> "Excellent", "Excellent", "Excellent", "Good"…
## $ CentralAirConditioning   <chr> "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Ye…
## $ `1stFloorSquareFeet`     <dbl> 856, 1262, 920, 961, 1145, 796, 1694, 1107, 1…
## $ `2ndFlrSquareFeet`       <dbl> 854, 0, 866, 756, 1053, 566, 0, 983, 752, 0, …
## $ LivAreaSquareFeet        <dbl> 1710, 1262, 1786, 1717, 2198, 1362, 1694, 209…
## $ FullBathrooms            <dbl> 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 3, 1, 2, 1, …
## $ Bedrooms                 <dbl> 3, 3, 3, 3, 4, 1, 3, 3, 2, 2, 3, 4, 2, 3, 2, …
## $ KitchenQualityCondition  <chr> "Good", "Typical/Average", "Good", "Good", "G…
## $ TotalRooms               <dbl> 8, 6, 6, 7, 9, 5, 7, 7, 8, 5, 5, 11, 4, 7, 5,…
## $ GarageArea               <dbl> 548, 460, 608, 642, 836, 480, 636, 484, 468, …
## $ TotalPorchAreaSquareFeet <dbl> 61, 0, 42, 307, 84, 30, 57, 432, 205, 4, 0, 2…
## $ MonthSold                <dbl> 2, 5, 9, 2, 12, 10, 8, 11, 4, 1, 2, 7, 9, 8, …
## $ YearSold                 <dbl> 2008, 2007, 2008, 2006, 2008, 2009, 2007, 200…
## $ SaleType                 <chr> "Warranty Deed - Conventional", "Warranty Dee…
## $ SaleCondition            <chr> "Normal", "Normal", "Normal", "Abnorml", "Nor…
## $ SalePrice                <dbl> 208500, 181500, 223500, 140000, 250000, 14300…

Glimpse gives the transposed summary of the data frame, giving a quick and readable view of the dataset.
It shows the data types and the first few values of each column, which is be very useful for getting an overview of the data.

str(House_pricing_data)

## tibble [1,460 × 26] (S3: tbl_df/tbl/data.frame)
##  $ HouseId                 : num [1:1460] 1 2 3 4 5 6 7 8 9 10 ...
##  $ MSZoning                : chr [1:1460] "Residential Low Density" "Residential Low Density" "Residential Low Density" "Residential Low Density" ...
##  $ LotAreaSquareFeet       : num [1:1460] 8450 9600 11250 9550 14260 ...
##  $ LandSlope               : chr [1:1460] "Gentleslope" "Gentleslope" "Gentleslope" "Gentleslope" ...
##  $ BuildingType            : chr [1:1460] "Single-family Detached" "Single-family Detached" "Single-family Detached" "Single-family Detached" ...
##  $ OverallCondition        : num [1:1460] 5 8 5 5 5 5 5 6 5 6 ...
##  $ YearBuilt               : num [1:1460] 2003 1976 2001 1915 2000 ...
##  $ ExteriorCondition       : chr [1:1460] "Average/Typical" "Average/Typical" "Average/Typical" "Average/Typical" ...
##  $ Foundation              : chr [1:1460] "Poured Contrete" "Cinder Block" "Poured Contrete" "Brick & Tile" ...
##  $ TotalBasementSquareFeet : num [1:1460] 856 1262 920 756 1145 ...
##  $ HeatingQualityCondition : chr [1:1460] "Excellent" "Excellent" "Excellent" "Good" ...
##  $ CentralAirConditioning  : chr [1:1460] "Yes" "Yes" "Yes" "Yes" ...
##  $ 1stFloorSquareFeet      : num [1:1460] 856 1262 920 961 1145 ...
##  $ 2ndFlrSquareFeet        : num [1:1460] 854 0 866 756 1053 ...
##  $ LivAreaSquareFeet       : num [1:1460] 1710 1262 1786 1717 2198 ...
##  $ FullBathrooms           : num [1:1460] 2 2 2 1 2 1 2 2 2 1 ...
##  $ Bedrooms                : num [1:1460] 3 3 3 3 4 1 3 3 2 2 ...
##  $ KitchenQualityCondition : chr [1:1460] "Good" "Typical/Average" "Good" "Good" ...
##  $ TotalRooms              : num [1:1460] 8 6 6 7 9 5 7 7 8 5 ...
##  $ GarageArea              : num [1:1460] 548 460 608 642 836 480 636 484 468 205 ...
##  $ TotalPorchAreaSquareFeet: num [1:1460] 61 0 42 307 84 30 57 432 205 4 ...
##  $ MonthSold               : num [1:1460] 2 5 9 2 12 10 8 11 4 1 ...
##  $ YearSold                : num [1:1460] 2008 2007 2008 2006 2008 ...
##  $ SaleType                : chr [1:1460] "Warranty Deed - Conventional" "Warranty Deed - Conventional" "Warranty Deed - Conventional" "Warranty Deed - Conventional" ...
##  $ SaleCondition           : chr [1:1460] "Normal" "Normal" "Normal" "Abnorml" ...
##  $ SalePrice               : num [1:1460] 208500 181500 223500 140000 250000 ...

We have 26 colums and 1460 rows.
The columns consists of num and char datatypes
We get to see the first few values of each column, allowing us to understand the kind of data each column holds.

summary(House_pricing_data)

##     HouseId         MSZoning         LotAreaSquareFeet  LandSlope        
##  Min.   :   1.0   Length:1460        Min.   :  1300    Length:1460       
##  1st Qu.: 365.8   Class :character   1st Qu.:  7554    Class :character  
##  Median : 730.5   Mode  :character   Median :  9478    Mode  :character  
##  Mean   : 730.5                      Mean   : 10517                      
##  3rd Qu.:1095.2                      3rd Qu.: 11602                      
##  Max.   :1460.0                      Max.   :215245                      
##  BuildingType       OverallCondition   YearBuilt    ExteriorCondition 
##  Length:1460        Min.   :1.000    Min.   :1872   Length:1460       
##  Class :character   1st Qu.:5.000    1st Qu.:1954   Class :character  
##  Mode  :character   Median :5.000    Median :1973   Mode  :character  
##                     Mean   :5.575    Mean   :1971                     
##                     3rd Qu.:6.000    3rd Qu.:2000                     
##                     Max.   :9.000    Max.   :2010                     
##   Foundation        TotalBasementSquareFeet HeatingQualityCondition
##  Length:1460        Min.   :   0.0          Length:1460            
##  Class :character   1st Qu.: 795.8          Class :character       
##  Mode  :character   Median : 991.5          Mode  :character       
##                     Mean   :1057.4                                 
##                     3rd Qu.:1298.2                                 
##                     Max.   :6110.0                                 
##  CentralAirConditioning 1stFloorSquareFeet 2ndFlrSquareFeet LivAreaSquareFeet
##  Length:1460            Min.   : 334       Min.   :   0     Min.   : 334     
##  Class :character       1st Qu.: 882       1st Qu.:   0     1st Qu.:1130     
##  Mode  :character       Median :1087       Median :   0     Median :1464     
##                         Mean   :1163       Mean   : 347     Mean   :1515     
##                         3rd Qu.:1391       3rd Qu.: 728     3rd Qu.:1777     
##                         Max.   :4692       Max.   :2065     Max.   :5642     
##  FullBathrooms      Bedrooms     KitchenQualityCondition   TotalRooms    
##  Min.   :0.000   Min.   :0.000   Length:1460             Min.   : 2.000  
##  1st Qu.:1.000   1st Qu.:2.000   Class :character        1st Qu.: 5.000  
##  Median :2.000   Median :3.000   Mode  :character        Median : 6.000  
##  Mean   :1.565   Mean   :2.866                           Mean   : 6.518  
##  3rd Qu.:2.000   3rd Qu.:3.000                           3rd Qu.: 7.000  
##  Max.   :3.000   Max.   :8.000                           Max.   :14.000  
##    GarageArea     TotalPorchAreaSquareFeet   MonthSold         YearSold   
##  Min.   :   0.0   Min.   :  0.00           Min.   : 1.000   Min.   :2006  
##  1st Qu.: 334.5   1st Qu.:  0.00           1st Qu.: 5.000   1st Qu.:2007  
##  Median : 480.0   Median : 40.00           Median : 6.000   Median :2008  
##  Mean   : 473.0   Mean   : 68.61           Mean   : 6.322   Mean   :2008  
##  3rd Qu.: 576.0   3rd Qu.:104.00           3rd Qu.: 8.000   3rd Qu.:2009  
##  Max.   :1418.0   Max.   :638.00           Max.   :12.000   Max.   :2010  
##    SaleType         SaleCondition        SalePrice     
##  Length:1460        Length:1460        Min.   : 34900  
##  Class :character   Class :character   1st Qu.:129975  
##  Mode  :character   Mode  :character   Median :163000  
##                                        Mean   :180921  
##                                        3rd Qu.:214000  
##                                        Max.   :755000

library(skimr) #  More detailed summary using skimr
skim(House_pricing_data)

Data summary
Name	House_pricing_data
Number of rows	1460
Number of columns	26
_______________________
Column type frequency:
character	10
numeric	16
________________________
Group variables	None

Variable type: character

skim_variable	complete_rate	min	max	n_unique
MSZoning	1	10	28	5
LandSlope	1	11	13	3
BuildingType	1	6	62	5
ExteriorCondition	1	4	15	5
Foundation	1	4	15	6
HeatingQualityCondition	1	4	15	5
CentralAirConditioning	1	2	3	2
KitchenQualityCondition	1	4	15	4
SaleType	1	5	42	9
SaleCondition	1	6	7	6

Variable type: numeric

skim_variable	complete_rate	mean	sd	p0	p25	p50	p75	p100	hist
HouseId	1	730.50	421.61	1	365.75	730.5	1095.25	1460	▇▇▇▇▇
LotAreaSquareFeet	1	10516.83	9981.26	1300	7553.50	9478.5	11601.50	215245	▇▁▁▁▁
OverallCondition	1	5.58	1.11	1	5.00	5.0	6.00	9	▁▁▇▅▁
YearBuilt	1	1971.27	30.20	1872	1954.00	1973.0	2000.00	2010	▁▂▃▆▇
TotalBasementSquareFeet	1	1057.43	438.71	0	795.75	991.5	1298.25	6110	▇▃▁▁▁
1stFloorSquareFeet	1	1162.63	386.59	334	882.00	1087.0	1391.25	4692	▇▅▁▁▁
2ndFlrSquareFeet	1	346.99	436.53	0	0.00	0.0	728.00	2065	▇▃▂▁▁
LivAreaSquareFeet	1	1515.46	525.48	334	1129.50	1464.0	1776.75	5642	▇▇▁▁▁
FullBathrooms	1	1.57	0.55	0	1.00	2.0	2.00	3	▁▇▁▇▁
Bedrooms	1	2.87	0.82	0	2.00	3.0	3.00	8	▁▇▂▁▁
TotalRooms	1	6.52	1.63	2	5.00	6.0	7.00	14	▂▇▇▁▁
GarageArea	1	472.98	213.80	0	334.50	480.0	576.00	1418	▂▇▃▁▁
TotalPorchAreaSquareFeet	1	68.61	85.86	0	0.00	40.0	104.00	638	▇▂▁▁▁
MonthSold	1	6.32	2.70	1	5.00	6.0	8.00	12	▃▆▇▃▃
YearSold	1	2007.82	1.33	2006	2007.00	2008.0	2009.00	2010	▇▇▇▇▅
SalePrice	1	180921.20	79442.50	34900	129975.00	163000.0	214000.00	755000	▇▅▁▁▁

CHECKING FOR DUPLICATES

sum(duplicated(House_pricing_data))

## [1] 0

There are no duplicates.

CHECKING FOR MISSING VALUES

sum(is.na(House_pricing_data))

## [1] 0

There are no missing values

VISUALIZATION

I will first separate the numerical columns and the categorical columns
Then ill drop “HouseId” since its redundant

# Separate numerical columns
numerical_cols <- House_pricing_data %>%
  select_if(is.numeric)

# Drop the HouseId column from the numerical_cols dataset
numerical_cols <- numerical_cols %>%
  select(-HouseId)
colnames(numerical_cols)

##  [1] "LotAreaSquareFeet"        "OverallCondition"        
##  [3] "YearBuilt"                "TotalBasementSquareFeet" 
##  [5] "1stFloorSquareFeet"       "2ndFlrSquareFeet"        
##  [7] "LivAreaSquareFeet"        "FullBathrooms"           
##  [9] "Bedrooms"                 "TotalRooms"              
## [11] "GarageArea"               "TotalPorchAreaSquareFeet"
## [13] "MonthSold"                "YearSold"                
## [15] "SalePrice"

head(numerical_cols)

## # A tibble: 6 × 15
##   LotAreaSquareFeet OverallCondition YearBuilt TotalBasementSquareFeet
##               <dbl>            <dbl>     <dbl>                   <dbl>
## 1              8450                5      2003                     856
## 2              9600                8      1976                    1262
## 3             11250                5      2001                     920
## 4              9550                5      1915                     756
## 5             14260                5      2000                    1145
## 6             14115                5      1993                     796
## # ℹ 11 more variables: `1stFloorSquareFeet` <dbl>, `2ndFlrSquareFeet` <dbl>,
## #   LivAreaSquareFeet <dbl>, FullBathrooms <dbl>, Bedrooms <dbl>,
## #   TotalRooms <dbl>, GarageArea <dbl>, TotalPorchAreaSquareFeet <dbl>,
## #   MonthSold <dbl>, YearSold <dbl>, SalePrice <dbl>

# Separate categorical columns
categorical_cols <- House_pricing_data %>%
  select_if(function(x) is.factor(x) | is.character(x))

colnames(categorical_cols)

##  [1] "MSZoning"                "LandSlope"              
##  [3] "BuildingType"            "ExteriorCondition"      
##  [5] "Foundation"              "HeatingQualityCondition"
##  [7] "CentralAirConditioning"  "KitchenQualityCondition"
##  [9] "SaleType"                "SaleCondition"

Visualize the Distribution of Numerical Variables

I will visualize using histograms

SalePrice Distribution and TotalBasementSquareFeet Distribution

# Create individual histograms for each numerical column
p1 <- ggplot(House_pricing_data, aes(x = SalePrice)) + 
  geom_histogram(fill = "blue", bins = 30, alpha = 0.5) + 
  ggtitle("SalePrice Distribution")

p2 <- ggplot(House_pricing_data, aes(x = TotalBasementSquareFeet)) + 
  geom_histogram(fill = "green", bins = 30, alpha = 0.5) + 
  ggtitle("TotalBasementSquareFeet Distribution")

grid.arrange(p1, p2)

Interpretation

1. SalePrice Distribution

Shape of the Distribution: The histogram appears to have a right-skewed distribution. Peak: There is a peak at lower sale prices, suggesting that most properties have a lower sale price. This could be typical of a market where there are many affordable properties.
Tail to the Right: There is a long tail extending toward higher sale prices. This indicates that a smaller number of properties have significantly higher sale prices.
Outliers: The tail also suggests the presence of outliers—properties with very high sale prices, which could be luxury homes or properties in very high-demand locations.
This distribution indicates a typical “few expensive properties, many affordable ones” scenario, which is often observed in housing markets.

2. TotalBasementSquareFeet Distribution

Shape of the Distribution: The histogram shows a skewed distribution that is left-skewed.
Peak near 0: The majority of homes have smaller basements, with many properties having no basement or a small basement. This is seen in the peak near the left side of the histogram (around 0 square feet).
Gradual decline: As the size of the basement increases, the frequency decreases, indicating that fewer homes have very large basements.
Small Tail on the Right: There are some homes with very large basements, but these properties are relatively rare. The right tail is smaller, suggesting that these larger basement sizes are outliers.

LotAreaSquareFeet Distribution and GarageArea Distribution

p3 <- ggplot(House_pricing_data, aes(x = LotAreaSquareFeet)) + 
  geom_histogram(fill = "red", bins = 30, alpha = 0.5) + 
  ggtitle("LotAreaSquareFeet Distribution")

p4 <- ggplot(House_pricing_data, aes(x = GarageArea)) + 
  geom_histogram(fill = "purple", bins = 30, alpha = 0.5) + 
  ggtitle("GarageArea Distribution")

grid.arrange(p3, p4)

Interpretation

1. LotAreaSquareFeet Distribution

Shape of Distribution: The histogram shows a right-skewed distribution.
Peak at Lower Values: Most houses have smaller lots, with a large peak near 0–10,000 square feet.
Long Tail to the Right: A few properties have significantly larger lots, as indicated by the long tail extending towards the right side of the histogram (up to 200,000 square feet).
Outliers: There may be a few extreme outliers (very large lots) which could represent estates or properties in special areas (e.g., rural or suburban locations).
This suggests that most properties are on average-sized lots, with fewer large properties on extensive land.

2. GarageArea Distribution

Shape of Distribution: The histogram appears to have a bi-modal distribution, with two distinct peaks.
Peak Near Zero: Many properties either have small garages or no garages at all (indicating garages may not be present in every home).
Peak at Moderate Garage Size: The second peak occurs around the 400-600 square foot range, which indicates a common garage size for most properties.
Right Tail: There are fewer properties with larger garages, as seen in the tail of the distribution extending to the right (with some properties having garage areas up to 1000 square feet). This suggests that many houses have smaller garages (or none at all), with a smaller group of houses having significantly larger garages.

LivAreaSquareFeet Distribution and 1stFloorSquareFeet Distribution

p5 <- ggplot(House_pricing_data, aes(x = LivAreaSquareFeet)) + 
  geom_histogram(fill = "orange", bins = 30, alpha = 0.5) + 
  ggtitle("LivAreaSquareFeet Distribution")

p6 <- ggplot(House_pricing_data, aes(x = `1stFloorSquareFeet`)) + 
  geom_histogram(fill = "yellow", bins = 30, alpha = 0.5) + 
  ggtitle("1stFloorSquareFeet Distribution")

grid.arrange(p5, p6)

Intrepretation

1. LivAreaSquareFeet Distribution

Shape of Distribution: The histogram appears to be slightly right-skewed with a peak around the 1,000–2,000 square foot range. Interpretation:
Peak between 1,000 and 2,000 sq. ft.: Most homes in the dataset have a living area within this range, indicating that this is a typical size for homes in the dataset.
Tail to the Right: The tail on the right side suggests that there are some homes with very large living areas (e.g., 3,000 to 6,000 square feet), but these homes are relatively rare.
Outliers: There are a few extreme outliers with very large living areas, which likely represent luxury or larger homes.
This distribution indicates that the majority of homes have a living area around the median size, with a few large homes pushing the upper end of the distribution.

2. 1stFloorSquareFeet Distribution

Shape of Distribution: The histogram shows a similar shape to the previous one but appears to have more concentration in the lower range (less than 2,000 sq. ft.).
Peak around 1,000–1,500 sq. ft.: Most homes have a first floor that is in the 1,000 to 1,500 square feet range, which is typical for many homes.
Skew to the Right: The right tail extends slightly, indicating that there are a few homes with larger first floors, but these properties are less common.
Lower Range Dominance: The distribution has more homes with smaller first floors, but there are still a few homes with larger first floors.
This suggests that many homes have a first floor that is of moderate size, and there are a few larger homes with significantly more square footage on the first floor.

OverallCondition Distribution and 2ndFlrSquareFeet Distribution

p7 <- ggplot(House_pricing_data, aes(x = OverallCondition)) + 
  geom_histogram(fill = "pink", bins = 30, alpha = 0.5) + 
  ggtitle("OverallCondition Distribution")

p8 <- ggplot(House_pricing_data, aes(x = `2ndFlrSquareFeet`)) + 
  geom_histogram(fill = "brown", bins = 30, alpha = 0.5) + 
  ggtitle("2ndFlrSquareFeet Distribution")

grid.arrange(p7, p8)

Interpretation

1. OverallCondition Distribution

Shape of Distribution: The histogram appears to be skewed with a peak at 5, and other values appearing much less frequently.
Peak at 5: The most common condition of the homes is 5 (likely indicating an average or standard condition). This is the mode of the data, showing that a large number of houses in the dataset are considered to be in “average” condition.
Smaller Peaks for Other Values: There are some other values (2.5, 7.5), but they occur far less frequently. This indicates that very few homes have a significantly lower or higher overall condition compared to the typical condition.
Outliers: Some homes have a very high or low condition score, but they are rare. This suggests that the majority of homes in the dataset are in an average condition, with fewer homes in either poor or excellent condition.

2. 2ndFlrSquareFeet Distribution

Shape of Distribution: The histogram shows a left-skewed distribution.
Peak at 0: A large number of homes have little to no second floor (or the second floor is very small), as shown by the peak at the lower end of the scale (near 0 square feet).
Gradual Increase: As the square footage increases, the frequency gradually decreases, with a small number of homes having larger second floors.
Right Tail: The tail on the right suggests a few homes have significantly larger second floors, but they are outliers.
This indicates that most homes in the dataset do not have a second floor or have a small second floor, while only a few homes have large second floors.

TotalPorchAreaSquareFeet Distribution and TotalRooms Distribution and FullBathrooms Distribution

p9 <- ggplot(House_pricing_data, aes(x = TotalPorchAreaSquareFeet)) + 
  geom_histogram(fill = "cyan", bins = 30, alpha = 0.5) + 
  ggtitle("TotalPorchAreaSquareFeet Distribution")

p10 <- ggplot(House_pricing_data, aes(x = TotalRooms)) + 
  geom_histogram(fill = "green", bins = 30, alpha = 0.5) + 
  ggtitle("TotalRooms Distribution")

p11 <- ggplot(House_pricing_data, aes(x = FullBathrooms)) + 
  geom_histogram(fill = "blue", bins = 30, alpha = 0.5) + 
  ggtitle("FullBathrooms Distribution")

grid.arrange(p9, p10, p11 )

Interpretation

1. TotalPorchAreaSquareFeet Distribution

Shape of Distribution: The histogram shows a left-skewed distribution.
Peak Near Zero: Most properties have small or no porch areas, with a peak at or near 0 square feet.
Tail on the Right: A few homes have significantly larger porch areas, as seen in the tail of the distribution extending towards the right (up to around 400 square feet).
Outliers: There are a few homes with unusually large porch areas, but these are rare.
This suggests that porches are either small or not present in many properties, with only a few homes featuring larger porch spaces.

2. TotalRooms Distribution

Shape of Distribution: The histogram is somewhat skewed, with a higher concentration of homes having between 5 and 7 rooms.
Peak at 5–7 Rooms: Most homes in the dataset have between 5 and 7 rooms, indicating this is the typical size for properties in the dataset.
Lower Frequency for More Rooms: There are fewer homes with a very high number of rooms (above 10), and these appear at the far right, forming a tail.
Outliers: Some properties may have many rooms, but these are not common.
This suggests that the typical home in this dataset has a moderate number of rooms, with some homes featuring larger numbers.

3. FullBathrooms Distribution

Shape of Distribution: The histogram shows a bimodal distribution, with two main peaks.
Peak at 1 and 2 Bathrooms: Most homes have either 1 or 2 full bathrooms, suggesting these are the most common bathroom configurations in the dataset.
Few Homes with More Bathrooms: Very few homes have more than 2 bathrooms (3 bathrooms are shown as outliers on the far right side of the histogram).
Zero Bathrooms: A small number of homes may have no full bathrooms, which could indicate properties under renovation or incomplete data.
This distribution indicates that most homes in this dataset have either 1 or 2 full bathrooms, with fewer homes having more.

COUNT PLOT FOR CATEGORICAL VARIABLES

Create count plots for each categorical variable

MSZoning Distribution and LandSlope Distribution

# Create count plots for each categorical variable  
c1 <- ggplot(House_pricing_data, aes(x = MSZoning, fill = MSZoning)) +
  geom_bar() + 
  ggtitle("MSZoning Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")

c2 <- ggplot(House_pricing_data, aes(x = LandSlope, fill = LandSlope)) +
  geom_bar() + 
  ggtitle("LandSlope Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")

grid.arrange(c1, c2)

INTERPRETATION

1. MSZoning Distribution

Residential Low Density (Blue): This category has the highest count of homes, indicating that the majority of properties in the dataset are zoned for residential low-density areas.
Residential High Density (Purple): This category has a moderate count, showing that a reasonable number of homes are in high-density residential areas, though not as many as in low-density.
Other Categories: There are also some homes in categories like Commercial (Red), Floating Village Residential (Green), and Residential Medium Density (Light Purple), but these have much lower counts compared to residential areas. Commercial has a very small number of homes, indicating that commercial zoning is not common for this dataset.

2. LandSlope Distribution

GentleSlope (Red): The vast majority of homes are located on gentle slopes, as indicated by the large count for this category. This suggests that most properties are built on relatively flat or mild slopes.
ModerateSlope (Green): A small number of homes are located on moderate slopes. This could indicate that a few properties are in more hilly or elevated areas, but it’s not very common.
SevereSlope (Blue): Very few homes are situated on severe slopes, as seen by the low count in this category.

BuildingType Distribution

c3 <- ggplot(House_pricing_data, aes(x = BuildingType, fill = BuildingType)) +
  geom_bar() + 
  ggtitle("BuildingType Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")
c3

INTERPRETATION

1. BuildingType Distribution

Single-Family Detached (Yellow): The most common building type, with over 1,000 instances. This indicates that the majority of properties in the dataset are single-family detached homes.
Duplex (Red): There are very few duplexes in the dataset, as indicated by the small count on the left.
Townhouse End Unit (Green): A relatively small number of homes are end units in townhouses.
Townhouse Inside Unit (Blue) and Two-family Conversion (Purple): These categories also have relatively low counts, showing that the dataset includes some but not many townhouses or properties converted from two-family homes.

ExteriorCondition Distribution

c4 <- ggplot(House_pricing_data, aes(x = ExteriorCondition, fill = ExteriorCondition)) +
  geom_bar() + 
  ggtitle("ExteriorCondition Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")

c4

INTERPRETATION

2. ExteriorCondition Distribution

Average/Typical (Red): The most common exterior condition for homes in this dataset, with a very high count. This indicates that most properties are in average condition.
Good (Blue): A smaller number of homes are in good condition.
Fair (Green): Very few homes are in fair condition.
Excellent (Yellow) and Poor (Purple): Extremely few homes fall under these categories, suggesting that very few homes in the dataset are in either excellent or poor condition.

Foundation Distribution and HeatingQualityCondition Distribution

c5 <- ggplot(House_pricing_data, aes(x = Foundation, fill = Foundation)) +
  geom_bar() + 
  ggtitle("Foundation Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")
c6 <- ggplot(House_pricing_data, aes(x = HeatingQualityCondition, fill = HeatingQualityCondition)) +
  geom_bar() + 
  ggtitle("HeatingQualityCondition Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")

grid.arrange(c5, c6)

INTERPRETATION

1. Foundation Distribution

Cinder Block (Yellow) and Poured Concrete (Green): The two most common foundation types, with a significant portion of homes having these foundation types.
Slab (Turquoise), Stone (Blue), and Wood (Purple): These foundation types are much less common, as indicated by their lower counts.

2. HeatingQualityCondition Distribution

Excellent (Green): The most common heating quality condition, with a high count. This suggests that most homes have excellent heating systems.
Average/Typical (Red): A smaller number of homes have typical heating conditions.
Good (Blue) and Fair (Green): These conditions are much less frequent, showing that good and fair heating systems are less common.
Poor (Purple): A very small number of homes have poor heating quality.

CentralAirConditioning Distribution and KitchenQualityCondition Distribution

c7 <- ggplot(House_pricing_data, aes(x = CentralAirConditioning, fill = CentralAirConditioning)) +
  geom_bar() + 
  ggtitle("CentralAirConditioning Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")

c8 <- ggplot(House_pricing_data, aes(x = KitchenQualityCondition, fill = KitchenQualityCondition)) +
  geom_bar() + 
  ggtitle("KitchenQualityCondition Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")

grid.arrange(c7, c8)

INTERPRETATION

1. CentralAirConditioning Distribution

Yes (Turquoise): The majority of homes in the dataset have central air conditioning (Yes), with a large count indicating that it’s a standard feature for most homes.
No (Red): Only a very small number of homes do not have central air conditioning. Interpretation:
The overwhelming majority of homes in the dataset have central air conditioning, suggesting it is a common feature in the properties.

2. KitchenQualityCondition Distribution

Typical/Average (Purple): The most common kitchen condition, with the highest count. This indicates that most homes have a kitchen of average quality.
Good (Blue): There is a smaller number of homes with good quality kitchens.
Fair (Green): A very small number of homes have fair quality kitchens.
Excellent (Red): Extremely few homes have excellent quality kitchens.
The majority of homes have average kitchens, with only a few homes having kitchens in good or fair conditions.
Excellent kitchens are quite rare.

SaleType Distribution

c9 <- ggplot(House_pricing_data, aes(x = SaleType, fill = SaleType)) +
  geom_bar() + 
  ggtitle("SaleType Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")
c9

INTERPRETATION

1. SaleType Distribution

Warranty Deed - Conventional (Pink): This category has the largest count, indicating that most properties in the dataset were sold with a warranty deed under conventional terms.
Down payment regular terms (Red), Contract Low Down (Yellow), Contract Low Interest (Green), and other categories: These have very few instances, showing that they are much less common sale types.

SaleCondition Distribution

c10 <- ggplot(House_pricing_data, aes(x = SaleCondition, fill = SaleCondition)) +
  geom_bar() + 
  ggtitle("SaleCondition Distribution") +
  theme(axis.text.x = element_text(angle = 45, hjust = 1), legend.position = "none")

c10

INTREPRETATION

1. SaleCondition Distribution

Normal (Blue): The vast majority of homes have a normal sale condition, as seen by the large count in this category.
Abnormal (Red), AdjLand (Yellow), Alloc (Green), Family (Teal), and Partial (Pink): These categories have very few homes, suggesting that these sale conditions are rare.
The normal sale condition is by far the most common in the dataset, meaning most properties were sold under typical circumstances.
Abnormal, AdjLand, Alloc, Family, and Partial conditions are relatively rare, indicating that these sale types are outliers.

CORRELATION HEATMAP

# Calculate the correlation matrix
cor_matrix <- cor(numerical_cols)
corrplot(cor_matrix, method = "color", type = "upper", 
         tl.col = "black", tl.srt = 45, 
         number.cex = 0.7)

Interpretation

SalePrice has strong positive correlations with LivAreaSquareFeet, GarageArea, and OverallCondition, meaning that larger homes with more rooms and in better condition tend to have higher prices.
Bedrooms and TotalRooms are highly correlated with each other, as expected, since more rooms typically mean more bedrooms.
YearBuilt shows moderate correlations with other variables, indicating that newer homes tend to have better features and higher prices.

Average SalePrice by Decade built

We have done feature engineering here. Creating Decade column

# Create a new column for the decade based on YearBuilt
House_pricing_data$Decade <- floor(House_pricing_data$YearBuilt / 10) * 10

# Calculate average SalePrice by Decade
average_saleprice_by_decade <- House_pricing_data %>%
  group_by(Decade) %>%
  summarise(average_saleprice = mean(SalePrice, na.rm = TRUE))

# Line chart for average SalePrice by Decade
ggplot(average_saleprice_by_decade, aes(x = factor(Decade), y = average_saleprice)) +
  geom_line(group = 1, color = "blue", linewidth = 1) +  # Line
  geom_point(color = "red", size = 2) +             # Points
  ggtitle("Average SalePrice by Decade of YearBuilt") +
  xlab("Decade Built") +                           
  ylab("Average Sale Price") +                     
  theme(axis.text.x = element_text(angle = 45, hjust = 1))

Interpretation

Initial Increase (1870–1890):

From the 1870s to the 1880s, there is a noticeable increase in average sale price. This suggests that properties built in the 1880s were more expensive than those built in earlier decades, which might indicate a growth in economic development or changes in property value during this period.

Sharp Decline (1890–1900):

From the 1890s to 1900s, there is a sharp drop in the average sale price. This could suggest a significant change in the market or economic conditions that led to a reduction in property values for homes built during this time.

Gradual Increase (1900–1930):

After the initial decline, we see a gradual rise in the average sale price, which continues through the 1930s. This could reflect gradual economic recovery or improvements in the housing market.

Stable and Low (1930–1970):

The average sale price remains relatively stable and low between the 1930s and 1970s. This period could represent more affordable housing conditions, with little fluctuation in prices, possibly due to market stability or economic factors like the Great Depression and post-war recovery.

Rapid Increase (1980–2010):

A rapid and steep rise in the average sale price begins around the 1980s, continuing into the 2000s and 2010s. This indicates a significant surge in home values, possibly due to factors like increased demand, inflation, and economic growth in these decades, which likely led to higher property prices.

Recent Outlier (2010):

The 2010 decade has a large jump in the average sale price, which might reflect changes in the housing market such as real estate booms, luxury home developments, or other market-driven factors specific to this period.

Average SalePrice by Number of Bedrooms

# Calculate average SalePrice by Number of Bedrooms
avg_saleprice_by_bedrooms <- House_pricing_data %>%
  group_by(Bedrooms) %>%
  summarise(average_saleprice = mean(SalePrice, na.rm = TRUE))

# Bar chart for SalePrice by Number of Bedrooms
ggplot(avg_saleprice_by_bedrooms, aes(x = factor(Bedrooms), y = average_saleprice)) + 
  geom_bar(stat = "identity", fill = "lightblue", color = "black") + 
  ggtitle("Average SalePrice by Number of Bedrooms") + 
  xlab("Number of Bedrooms") + 
  ylab("Average Sale Price") + 
  theme_minimal()

INTERPRETATION

Higher Sale Price for 0 Bedrooms (200,000+):

The bar for 0 bedrooms is the highest, with an average sale price of over $200,000. This suggests that homes listed as having 0 bedrooms might either be very small homes (like studios) or properties with unusual configurations that are still priced relatively high, potentially due to location or other factors.

Relatively Higher Sale Prices for 4 and 3 Bedrooms:

The 4-bedroom homes have a high average sale price, somewhat close to the 0-bedroom properties. 3-bedroom homes also have a relatively high average sale price.
These two bedroom categories likely represent family homes or moderately large homes that are valued higher.

Moderate Sale Prices for 2 and 5 Bedrooms:

Homes with 2 bedrooms have a moderate average sale price, slightly below 3 and 4-bedroom properties.
5-bedroom homes also have a relatively moderate sale price. This suggests that larger homes (5 bedrooms) do not necessarily command a higher price compared to moderately sized homes (3 or 4 bedrooms), possibly due to factors like location or the extra maintenance costs associated with larger homes.

Lower Sale Price for 6 and 8 Bedrooms:

The 6-bedroom and 8-bedroom homes have lower average sale prices compared to other bedroom counts. This might be due to a smaller sample size or a market segment where larger homes are priced lower (possibly because they require more maintenance or are not located in high-demand areas).

Average SalePrice by Number of FullBathrooms

# Calculate average SalePrice by Number of FullBathrooms
avg_saleprice_by_fullbathrooms <- House_pricing_data %>%
  group_by(FullBathrooms) %>%
  summarise(average_saleprice = mean(SalePrice, na.rm = TRUE))

# Bar chart for SalePrice by Number of FullBathrooms
ggplot(avg_saleprice_by_fullbathrooms, aes(x = factor(FullBathrooms), y = average_saleprice)) + 
  geom_bar(stat = "identity", fill = "lightgreen", color = "black") + 
  ggtitle("Average SalePrice by Number of FullBathrooms") + 
  xlab("Number of FullBathrooms") + 
  ylab("Average Sale Price") + 
  theme_minimal()

INTERPRETATION

0 Full Bathrooms:

Homes with 0 full bathrooms have an average sale price of around $200,000. This could reflect smaller properties like studios or homes where bathrooms are not considered full (e.g., half-baths or other non-traditional setups). However, the price is relatively high for homes with no full bathrooms, which could be driven by other factors like location or lot size.

1 Full Bathroom:

Homes with 1 full bathroom have an average sale price just above $150,000. These homes tend to be more affordable than those with more bathrooms, but the price is still significantly higher than for homes with 0 bathrooms, suggesting that adding a full bathroom increases the property’s value.

2 Full Bathrooms:

Homes with 2 full bathrooms show a noticeable increase in the average sale price to around $200,000. This suggests that having 2 full bathrooms in a house is a significant factor in increasing the home value, likely because it meets the needs of a larger family or adds convenience.

3 Full Bathrooms:

Homes with 3 full bathrooms have the highest average sale price of around $220,000. This could indicate that homes with more than 2 full bathrooms tend to be larger and have more luxury features, making them more expensive.

General Conclusion:

Homes with more full bathrooms tend to have higher average sale prices, reflecting that bathrooms are an important feature in determining the value of a property.
Homes with 3 full bathrooms appear to have the highest sale prices, possibly due to being larger homes suitable for bigger families or offering more amenities.
Homes with fewer bathrooms (0 or 1) tend to have lower average sale prices, which may indicate smaller properties or older homes with fewer modern conveniences.

# Calculate average SalePrice by TotalRooms
avg_saleprice_by_totalrooms <- House_pricing_data %>%
  group_by(TotalRooms) %>%
  summarise(average_saleprice = mean(SalePrice, na.rm = TRUE))

# Bar chart for SalePrice by TotalRooms
ggplot(avg_saleprice_by_totalrooms, aes(x = factor(TotalRooms), y = average_saleprice)) + 
  geom_bar(stat = "identity", fill = "lightblue", color = "black") + 
  ggtitle("Average SalePrice by TotalRooms") + 
  xlab("Number of Total Rooms") + 
  ylab("Average Sale Price") + 
  theme_minimal()

INTERPRETATION

Increase in Sale Price with More Rooms:

The average sale price increases as the number of total rooms increases. Homes with more rooms tend to have higher sale prices, which makes sense as larger homes usually come with higher values due to their larger size and increased functionality.

Moderate Increase:

The bar chart shows a moderate increase in the average sale price starting from 2 rooms and continuing to 9 or 10 rooms. After 9 rooms, the trend becomes relatively flat, suggesting that homes with 9 to 11 rooms have similar average prices, indicating that factors other than the number of rooms (such as location, age of the home, or other amenities) may also influence the price.

Drop in Price at 12 and 14 Rooms:

There is a sharp drop in average sale price for homes with 12 and 14 rooms, which might be due to several factors. Larger homes might be harder to sell in some markets, possibly due to higher maintenance costs, lower demand for such large homes, or the type of buyers who prefer smaller, more manageable homes. It could also reflect the data’s distribution, where the sample size for homes with these numbers of rooms might be smaller.

FEATURE ENGINEERING

We can do feature engineering to get total living area

# Create the TotalLivingArea feature by summing LivAreaSquareFeet and TotalBasementSquareFeet
House_pricing_data$TotalLivingArea <- House_pricing_data$LivAreaSquareFeet + House_pricing_data$TotalBasementSquareFeet

# Check the new feature by viewing the first few rows of the data
head(House_pricing_data$TotalLivingArea)

## [1] 2566 2524 2706 2473 3343 2158

# Scatter plot to explore the relationship between TotalLivingArea and SalePrice
ggplot(House_pricing_data, aes(x = TotalLivingArea, y = SalePrice)) +
  geom_point(color = "blue", alpha = 0.5) + 
  ggtitle("TotalLivingArea vs SalePrice") + 
  xlab("Total Living Area (sq ft)") + 
  ylab("Sale Price") + 
  theme_minimal()

INTERPRETATION

Positive Correlation:

As the TotalLivingArea (sq ft) increases, the SalePrice tends to increase as well. Larger homes, represented by higher values of TotalLivingArea, have higher SalePrice values.

Linear Trend:

The scatter plot displays a relatively linear trend, especially for homes with TotalLivingArea below 4000 square feet. This suggests that for most properties, each additional square foot of living area corresponds to a predictable increase in sale price.

Outliers:

There are a few outliers on the higher end of the TotalLivingArea scale, with SalePrice values that seem to deviate from the general trend. These could represent luxury or high-end properties with a much higher price relative to their size. These outliers may be due to unique properties (e.g., high-end finishes, locations, or amenities).

Data Concentration:

The plot shows a concentration of data points within the range of 0 to 4000 square feet, and after that, the frequency of points begins to decrease as the living area increases. This suggests that larger homes (with TotalLivingArea above 4000 sq ft) are less common in the dataset.

Group_2_ASSIGNMENT_1

Mercy Cheptoo

2025-03-02

GROUP MEMBERS

1. Mercy Cheptoo 21/05823

2. Edwin Mucheru 21/06264

3. Celine Salesa 21/08374

4. JoyComfort Wangari 21/05738

IMPORTING THE DATASET

EDA

CHECKING FOR DUPLICATES

CHECKING FOR MISSING VALUES

VISUALIZATION

Visualize the Distribution of Numerical Variables

SalePrice Distribution and TotalBasementSquareFeet Distribution

Interpretation

1. SalePrice Distribution

2. TotalBasementSquareFeet Distribution

LotAreaSquareFeet Distribution and GarageArea Distribution

Interpretation

1. LotAreaSquareFeet Distribution

2. GarageArea Distribution

LivAreaSquareFeet Distribution and 1stFloorSquareFeet Distribution

Intrepretation

1. LivAreaSquareFeet Distribution

2. 1stFloorSquareFeet Distribution

OverallCondition Distribution and 2ndFlrSquareFeet Distribution

Interpretation

1. OverallCondition Distribution

2. 2ndFlrSquareFeet Distribution

TotalPorchAreaSquareFeet Distribution and TotalRooms Distribution and FullBathrooms Distribution

Interpretation

1. TotalPorchAreaSquareFeet Distribution

2. TotalRooms Distribution

3. FullBathrooms Distribution

COUNT PLOT FOR CATEGORICAL VARIABLES

MSZoning Distribution and LandSlope Distribution

INTERPRETATION

1. MSZoning Distribution

2. LandSlope Distribution

BuildingType Distribution

INTERPRETATION

1. BuildingType Distribution

ExteriorCondition Distribution

INTERPRETATION

2. ExteriorCondition Distribution

Foundation Distribution and HeatingQualityCondition Distribution

INTERPRETATION

1. Foundation Distribution

2. HeatingQualityCondition Distribution

CentralAirConditioning Distribution and KitchenQualityCondition Distribution

INTERPRETATION

1. CentralAirConditioning Distribution

2. KitchenQualityCondition Distribution

SaleType Distribution

INTERPRETATION

1. SaleType Distribution

SaleCondition Distribution

INTREPRETATION

1. SaleCondition Distribution

CORRELATION HEATMAP

Interpretation

Average SalePrice by Decade built

Interpretation

Initial Increase (1870–1890):

Sharp Decline (1890–1900):

Gradual Increase (1900–1930):

Stable and Low (1930–1970):

Rapid Increase (1980–2010):

Recent Outlier (2010):

Average SalePrice by Number of Bedrooms

INTERPRETATION

Higher Sale Price for 0 Bedrooms (200,000+):

Relatively Higher Sale Prices for 4 and 3 Bedrooms:

Moderate Sale Prices for 2 and 5 Bedrooms:

Lower Sale Price for 6 and 8 Bedrooms:

Average SalePrice by Number of FullBathrooms

INTERPRETATION

0 Full Bathrooms:

1 Full Bathroom: