The dataset consisting of a single file, ames_prices.csv, and a data dictionary data-dictionary.txt. This dataset contains the sales price of each home as well as other attributes of the home and the sales transaction, such as the lot size, the square footage of each floor, when the home was built and remodeled, whether the kitchen is upgraded, etc. A data dictionary has been included with the data.

These variables are closely associated with the sales price of the home. This dataset is a model dataset for demonstrating machine learning techniques and for prediction.

Here our goal is to use a simple statistical model to tell a story about the factors that affect housing prices. I want you to build a linear regression/generalized linear model that incorporates several variables that influence housing prices (you should include the most influential factors on housing prices such as square footage, overall quality, lot size, type of sale, etc, but also pick a few smaller factors whose marginal effects can be calculated and plotted such as garage size or kitchen quality), and then make model visualizations to tell your story. I highly encourage you to use the marginaleffects package to help with making visualizations. If you see fit, you can also use dimensionality reduction techniques to improve your understanding of the dataset.

Note: For this project marginaleffects package was not used due to R studio version issues.

## Warning: package 'ggplot2' was built under R version 4.4.3

## Warning: package 'dplyr' was built under R version 4.4.3

## 
## 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

## Warning: package 'readr' was built under R version 4.4.2

## Rows: 1460 Columns: 81

## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## chr (43): MSZoning, Street, Alley, LotShape, LandContour, Utilities, LotConf...
## dbl (38): Id, MSSubClass, LotFrontage, LotArea, OverallQual, OverallCond, Ye...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

## # A tibble: 6 × 81
##      Id MSSubClass MSZoning LotFrontage LotArea Street Alley LotShape
##   <dbl>      <dbl> <chr>          <dbl>   <dbl> <chr>  <chr> <chr>   
## 1     1         60 RL                65    8450 Pave   <NA>  Reg     
## 2     2         20 RL                80    9600 Pave   <NA>  Reg     
## 3     3         60 RL                68   11250 Pave   <NA>  IR1     
## 4     4         70 RL                60    9550 Pave   <NA>  IR1     
## 5     5         60 RL                84   14260 Pave   <NA>  IR1     
## 6     6         50 RL                85   14115 Pave   <NA>  IR1     
## # ℹ 73 more variables: LandContour <chr>, Utilities <chr>, LotConfig <chr>,
## #   LandSlope <chr>, Neighborhood <chr>, Condition1 <chr>, Condition2 <chr>,
## #   BldgType <chr>, HouseStyle <chr>, OverallQual <dbl>, OverallCond <dbl>,
## #   YearBuilt <dbl>, YearRemodAdd <dbl>, RoofStyle <chr>, RoofMatl <chr>,
## #   Exterior1st <chr>, Exterior2nd <chr>, MasVnrType <chr>, MasVnrArea <dbl>,
## #   ExterQual <chr>, ExterCond <chr>, Foundation <chr>, BsmtQual <chr>,
## #   BsmtCond <chr>, BsmtExposure <chr>, BsmtFinType1 <chr>, BsmtFinSF1 <dbl>, …

## Rows: 1,460
## Columns: 81
## $ Id            <dbl> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1…
## $ MSSubClass    <dbl> 60, 20, 60, 70, 60, 50, 20, 60, 50, 190, 20, 60, 20, 20,…
## $ MSZoning      <chr> "RL", "RL", "RL", "RL", "RL", "RL", "RL", "RL", "RM", "R…
## $ LotFrontage   <dbl> 65, 80, 68, 60, 84, 85, 75, NA, 51, 50, 70, 85, NA, 91, …
## $ LotArea       <dbl> 8450, 9600, 11250, 9550, 14260, 14115, 10084, 10382, 612…
## $ Street        <chr> "Pave", "Pave", "Pave", "Pave", "Pave", "Pave", "Pave", …
## $ Alley         <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
## $ LotShape      <chr> "Reg", "Reg", "IR1", "IR1", "IR1", "IR1", "Reg", "IR1", …
## $ LandContour   <chr> "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", …
## $ Utilities     <chr> "AllPub", "AllPub", "AllPub", "AllPub", "AllPub", "AllPu…
## $ LotConfig     <chr> "Inside", "FR2", "Inside", "Corner", "FR2", "Inside", "I…
## $ LandSlope     <chr> "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", …
## $ Neighborhood  <chr> "CollgCr", "Veenker", "CollgCr", "Crawfor", "NoRidge", "…
## $ Condition1    <chr> "Norm", "Feedr", "Norm", "Norm", "Norm", "Norm", "Norm",…
## $ Condition2    <chr> "Norm", "Norm", "Norm", "Norm", "Norm", "Norm", "Norm", …
## $ BldgType      <chr> "1Fam", "1Fam", "1Fam", "1Fam", "1Fam", "1Fam", "1Fam", …
## $ HouseStyle    <chr> "2Story", "1Story", "2Story", "2Story", "2Story", "1.5Fi…
## $ OverallQual   <dbl> 7, 6, 7, 7, 8, 5, 8, 7, 7, 5, 5, 9, 5, 7, 6, 7, 6, 4, 5,…
## $ OverallCond   <dbl> 5, 8, 5, 5, 5, 5, 5, 6, 5, 6, 5, 5, 6, 5, 5, 8, 7, 5, 5,…
## $ YearBuilt     <dbl> 2003, 1976, 2001, 1915, 2000, 1993, 2004, 1973, 1931, 19…
## $ YearRemodAdd  <dbl> 2003, 1976, 2002, 1970, 2000, 1995, 2005, 1973, 1950, 19…
## $ RoofStyle     <chr> "Gable", "Gable", "Gable", "Gable", "Gable", "Gable", "G…
## $ RoofMatl      <chr> "CompShg", "CompShg", "CompShg", "CompShg", "CompShg", "…
## $ Exterior1st   <chr> "VinylSd", "MetalSd", "VinylSd", "Wd Sdng", "VinylSd", "…
## $ Exterior2nd   <chr> "VinylSd", "MetalSd", "VinylSd", "Wd Shng", "VinylSd", "…
## $ MasVnrType    <chr> "BrkFace", "None", "BrkFace", "None", "BrkFace", "None",…
## $ MasVnrArea    <dbl> 196, 0, 162, 0, 350, 0, 186, 240, 0, 0, 0, 286, 0, 306, …
## $ ExterQual     <chr> "Gd", "TA", "Gd", "TA", "Gd", "TA", "Gd", "TA", "TA", "T…
## $ ExterCond     <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "T…
## $ Foundation    <chr> "PConc", "CBlock", "PConc", "BrkTil", "PConc", "Wood", "…
## $ BsmtQual      <chr> "Gd", "Gd", "Gd", "TA", "Gd", "Gd", "Ex", "Gd", "TA", "T…
## $ BsmtCond      <chr> "TA", "TA", "TA", "Gd", "TA", "TA", "TA", "TA", "TA", "T…
## $ BsmtExposure  <chr> "No", "Gd", "Mn", "No", "Av", "No", "Av", "Mn", "No", "N…
## $ BsmtFinType1  <chr> "GLQ", "ALQ", "GLQ", "ALQ", "GLQ", "GLQ", "GLQ", "ALQ", …
## $ BsmtFinSF1    <dbl> 706, 978, 486, 216, 655, 732, 1369, 859, 0, 851, 906, 99…
## $ BsmtFinType2  <chr> "Unf", "Unf", "Unf", "Unf", "Unf", "Unf", "Unf", "BLQ", …
## $ BsmtFinSF2    <dbl> 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ BsmtUnfSF     <dbl> 150, 284, 434, 540, 490, 64, 317, 216, 952, 140, 134, 17…
## $ TotalBsmtSF   <dbl> 856, 1262, 920, 756, 1145, 796, 1686, 1107, 952, 991, 10…
## $ Heating       <chr> "GasA", "GasA", "GasA", "GasA", "GasA", "GasA", "GasA", …
## $ HeatingQC     <chr> "Ex", "Ex", "Ex", "Gd", "Ex", "Ex", "Ex", "Ex", "Gd", "E…
## $ CentralAir    <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "…
## $ Electrical    <chr> "SBrkr", "SBrkr", "SBrkr", "SBrkr", "SBrkr", "SBrkr", "S…
## $ `1stFlrSF`    <dbl> 856, 1262, 920, 961, 1145, 796, 1694, 1107, 1022, 1077, …
## $ `2ndFlrSF`    <dbl> 854, 0, 866, 756, 1053, 566, 0, 983, 752, 0, 0, 1142, 0,…
## $ LowQualFinSF  <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ GrLivArea     <dbl> 1710, 1262, 1786, 1717, 2198, 1362, 1694, 2090, 1774, 10…
## $ BsmtFullBath  <dbl> 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1,…
## $ BsmtHalfBath  <dbl> 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ FullBath      <dbl> 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1,…
## $ HalfBath      <dbl> 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1,…
## $ BedroomAbvGr  <dbl> 3, 3, 3, 3, 4, 1, 3, 3, 2, 2, 3, 4, 2, 3, 2, 2, 2, 2, 3,…
## $ KitchenAbvGr  <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1,…
## $ KitchenQual   <chr> "Gd", "TA", "Gd", "Gd", "Gd", "TA", "Gd", "TA", "TA", "T…
## $ TotRmsAbvGrd  <dbl> 8, 6, 6, 7, 9, 5, 7, 7, 8, 5, 5, 11, 4, 7, 5, 5, 5, 6, 6…
## $ Functional    <chr> "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", …
## $ Fireplaces    <dbl> 0, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 2, 0, 1, 1, 0, 1, 0, 0,…
## $ FireplaceQu   <chr> NA, "TA", "TA", "Gd", "TA", NA, "Gd", "TA", "TA", "TA", …
## $ GarageType    <chr> "Attchd", "Attchd", "Attchd", "Detchd", "Attchd", "Attch…
## $ GarageYrBlt   <dbl> 2003, 1976, 2001, 1998, 2000, 1993, 2004, 1973, 1931, 19…
## $ GarageFinish  <chr> "RFn", "RFn", "RFn", "Unf", "RFn", "Unf", "RFn", "RFn", …
## $ GarageCars    <dbl> 2, 2, 2, 3, 3, 2, 2, 2, 2, 1, 1, 3, 1, 3, 1, 2, 2, 2, 2,…
## $ GarageArea    <dbl> 548, 460, 608, 642, 836, 480, 636, 484, 468, 205, 384, 7…
## $ GarageQual    <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "Fa", "G…
## $ GarageCond    <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "T…
## $ PavedDrive    <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "…
## $ WoodDeckSF    <dbl> 0, 298, 0, 0, 192, 40, 255, 235, 90, 0, 0, 147, 140, 160…
## $ OpenPorchSF   <dbl> 61, 0, 42, 35, 84, 30, 57, 204, 0, 4, 0, 21, 0, 33, 213,…
## $ EnclosedPorch <dbl> 0, 0, 0, 272, 0, 0, 0, 228, 205, 0, 0, 0, 0, 0, 176, 0, …
## $ `3SsnPorch`   <dbl> 0, 0, 0, 0, 0, 320, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ ScreenPorch   <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, …
## $ PoolArea      <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,…
## $ PoolQC        <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …
## $ Fence         <chr> NA, NA, NA, NA, NA, "MnPrv", NA, NA, NA, NA, NA, NA, NA,…
## $ MiscFeature   <chr> NA, NA, NA, NA, NA, "Shed", NA, "Shed", NA, NA, NA, NA, …
## $ MiscVal       <dbl> 0, 0, 0, 0, 0, 700, 0, 350, 0, 0, 0, 0, 0, 0, 0, 0, 700,…
## $ MoSold        <dbl> 2, 5, 9, 2, 12, 10, 8, 11, 4, 1, 2, 7, 9, 8, 5, 7, 3, 10…
## $ YrSold        <dbl> 2008, 2007, 2008, 2006, 2008, 2009, 2007, 2009, 2008, 20…
## $ SaleType      <chr> "WD", "WD", "WD", "WD", "WD", "WD", "WD", "WD", "WD", "W…
## $ SaleCondition <chr> "Normal", "Normal", "Normal", "Abnorml", "Normal", "Norm…
## $ SalePrice     <dbl> 208500, 181500, 223500, 140000, 250000, 143000, 307000, …

##        Id           MSSubClass      MSZoning          LotFrontage    
##  Min.   :   1.0   Min.   : 20.0   Length:1460        Min.   : 21.00  
##  1st Qu.: 365.8   1st Qu.: 20.0   Class :character   1st Qu.: 59.00  
##  Median : 730.5   Median : 50.0   Mode  :character   Median : 69.00  
##  Mean   : 730.5   Mean   : 56.9                      Mean   : 70.05  
##  3rd Qu.:1095.2   3rd Qu.: 70.0                      3rd Qu.: 80.00  
##  Max.   :1460.0   Max.   :190.0                      Max.   :313.00  
##                                                      NA's   :259     
##     LotArea          Street             Alley             LotShape        
##  Min.   :  1300   Length:1460        Length:1460        Length:1460       
##  1st Qu.:  7554   Class :character   Class :character   Class :character  
##  Median :  9478   Mode  :character   Mode  :character   Mode  :character  
##  Mean   : 10517                                                           
##  3rd Qu.: 11602                                                           
##  Max.   :215245                                                           
##                                                                           
##  LandContour         Utilities          LotConfig          LandSlope        
##  Length:1460        Length:1460        Length:1460        Length:1460       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##                                                                             
##  Neighborhood        Condition1         Condition2          BldgType        
##  Length:1460        Length:1460        Length:1460        Length:1460       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##                                                                             
##   HouseStyle         OverallQual      OverallCond      YearBuilt   
##  Length:1460        Min.   : 1.000   Min.   :1.000   Min.   :1872  
##  Class :character   1st Qu.: 5.000   1st Qu.:5.000   1st Qu.:1954  
##  Mode  :character   Median : 6.000   Median :5.000   Median :1973  
##                     Mean   : 6.099   Mean   :5.575   Mean   :1971  
##                     3rd Qu.: 7.000   3rd Qu.:6.000   3rd Qu.:2000  
##                     Max.   :10.000   Max.   :9.000   Max.   :2010  
##                                                                    
##   YearRemodAdd   RoofStyle           RoofMatl         Exterior1st       
##  Min.   :1950   Length:1460        Length:1460        Length:1460       
##  1st Qu.:1967   Class :character   Class :character   Class :character  
##  Median :1994   Mode  :character   Mode  :character   Mode  :character  
##  Mean   :1985                                                           
##  3rd Qu.:2004                                                           
##  Max.   :2010                                                           
##                                                                         
##  Exterior2nd         MasVnrType          MasVnrArea      ExterQual        
##  Length:1460        Length:1460        Min.   :   0.0   Length:1460       
##  Class :character   Class :character   1st Qu.:   0.0   Class :character  
##  Mode  :character   Mode  :character   Median :   0.0   Mode  :character  
##                                        Mean   : 103.7                     
##                                        3rd Qu.: 166.0                     
##                                        Max.   :1600.0                     
##                                        NA's   :8                          
##   ExterCond          Foundation          BsmtQual           BsmtCond        
##  Length:1460        Length:1460        Length:1460        Length:1460       
##  Class :character   Class :character   Class :character   Class :character  
##  Mode  :character   Mode  :character   Mode  :character   Mode  :character  
##                                                                             
##                                                                             
##                                                                             
##                                                                             
##  BsmtExposure       BsmtFinType1         BsmtFinSF1     BsmtFinType2      
##  Length:1460        Length:1460        Min.   :   0.0   Length:1460       
##  Class :character   Class :character   1st Qu.:   0.0   Class :character  
##  Mode  :character   Mode  :character   Median : 383.5   Mode  :character  
##                                        Mean   : 443.6                     
##                                        3rd Qu.: 712.2                     
##                                        Max.   :5644.0                     
##                                                                           
##    BsmtFinSF2        BsmtUnfSF       TotalBsmtSF       Heating         
##  Min.   :   0.00   Min.   :   0.0   Min.   :   0.0   Length:1460       
##  1st Qu.:   0.00   1st Qu.: 223.0   1st Qu.: 795.8   Class :character  
##  Median :   0.00   Median : 477.5   Median : 991.5   Mode  :character  
##  Mean   :  46.55   Mean   : 567.2   Mean   :1057.4                     
##  3rd Qu.:   0.00   3rd Qu.: 808.0   3rd Qu.:1298.2                     
##  Max.   :1474.00   Max.   :2336.0   Max.   :6110.0                     
##                                                                        
##   HeatingQC          CentralAir         Electrical           1stFlrSF   
##  Length:1460        Length:1460        Length:1460        Min.   : 334  
##  Class :character   Class :character   Class :character   1st Qu.: 882  
##  Mode  :character   Mode  :character   Mode  :character   Median :1087  
##                                                           Mean   :1163  
##                                                           3rd Qu.:1391  
##                                                           Max.   :4692  
##                                                                         
##     2ndFlrSF     LowQualFinSF       GrLivArea     BsmtFullBath   
##  Min.   :   0   Min.   :  0.000   Min.   : 334   Min.   :0.0000  
##  1st Qu.:   0   1st Qu.:  0.000   1st Qu.:1130   1st Qu.:0.0000  
##  Median :   0   Median :  0.000   Median :1464   Median :0.0000  
##  Mean   : 347   Mean   :  5.845   Mean   :1515   Mean   :0.4253  
##  3rd Qu.: 728   3rd Qu.:  0.000   3rd Qu.:1777   3rd Qu.:1.0000  
##  Max.   :2065   Max.   :572.000   Max.   :5642   Max.   :3.0000  
##                                                                  
##   BsmtHalfBath        FullBath        HalfBath       BedroomAbvGr  
##  Min.   :0.00000   Min.   :0.000   Min.   :0.0000   Min.   :0.000  
##  1st Qu.:0.00000   1st Qu.:1.000   1st Qu.:0.0000   1st Qu.:2.000  
##  Median :0.00000   Median :2.000   Median :0.0000   Median :3.000  
##  Mean   :0.05753   Mean   :1.565   Mean   :0.3829   Mean   :2.866  
##  3rd Qu.:0.00000   3rd Qu.:2.000   3rd Qu.:1.0000   3rd Qu.:3.000  
##  Max.   :2.00000   Max.   :3.000   Max.   :2.0000   Max.   :8.000  
##                                                                    
##   KitchenAbvGr   KitchenQual         TotRmsAbvGrd     Functional       
##  Min.   :0.000   Length:1460        Min.   : 2.000   Length:1460       
##  1st Qu.:1.000   Class :character   1st Qu.: 5.000   Class :character  
##  Median :1.000   Mode  :character   Median : 6.000   Mode  :character  
##  Mean   :1.047                      Mean   : 6.518                     
##  3rd Qu.:1.000                      3rd Qu.: 7.000                     
##  Max.   :3.000                      Max.   :14.000                     
##                                                                        
##    Fireplaces    FireplaceQu         GarageType         GarageYrBlt  
##  Min.   :0.000   Length:1460        Length:1460        Min.   :1900  
##  1st Qu.:0.000   Class :character   Class :character   1st Qu.:1961  
##  Median :1.000   Mode  :character   Mode  :character   Median :1980  
##  Mean   :0.613                                         Mean   :1979  
##  3rd Qu.:1.000                                         3rd Qu.:2002  
##  Max.   :3.000                                         Max.   :2010  
##                                                        NA's   :81    
##  GarageFinish         GarageCars      GarageArea      GarageQual       
##  Length:1460        Min.   :0.000   Min.   :   0.0   Length:1460       
##  Class :character   1st Qu.:1.000   1st Qu.: 334.5   Class :character  
##  Mode  :character   Median :2.000   Median : 480.0   Mode  :character  
##                     Mean   :1.767   Mean   : 473.0                     
##                     3rd Qu.:2.000   3rd Qu.: 576.0                     
##                     Max.   :4.000   Max.   :1418.0                     
##                                                                        
##   GarageCond         PavedDrive          WoodDeckSF      OpenPorchSF    
##  Length:1460        Length:1460        Min.   :  0.00   Min.   :  0.00  
##  Class :character   Class :character   1st Qu.:  0.00   1st Qu.:  0.00  
##  Mode  :character   Mode  :character   Median :  0.00   Median : 25.00  
##                                        Mean   : 94.24   Mean   : 46.66  
##                                        3rd Qu.:168.00   3rd Qu.: 68.00  
##                                        Max.   :857.00   Max.   :547.00  
##                                                                         
##  EnclosedPorch      3SsnPorch       ScreenPorch        PoolArea      
##  Min.   :  0.00   Min.   :  0.00   Min.   :  0.00   Min.   :  0.000  
##  1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.00   1st Qu.:  0.000  
##  Median :  0.00   Median :  0.00   Median :  0.00   Median :  0.000  
##  Mean   : 21.95   Mean   :  3.41   Mean   : 15.06   Mean   :  2.759  
##  3rd Qu.:  0.00   3rd Qu.:  0.00   3rd Qu.:  0.00   3rd Qu.:  0.000  
##  Max.   :552.00   Max.   :508.00   Max.   :480.00   Max.   :738.000  
##                                                                      
##     PoolQC             Fence           MiscFeature           MiscVal        
##  Length:1460        Length:1460        Length:1460        Min.   :    0.00  
##  Class :character   Class :character   Class :character   1st Qu.:    0.00  
##  Mode  :character   Mode  :character   Mode  :character   Median :    0.00  
##                                                           Mean   :   43.49  
##                                                           3rd Qu.:    0.00  
##                                                           Max.   :15500.00  
##                                                                             
##      MoSold           YrSold       SaleType         SaleCondition     
##  Min.   : 1.000   Min.   :2006   Length:1460        Length:1460       
##  1st Qu.: 5.000   1st Qu.:2007   Class :character   Class :character  
##  Median : 6.000   Median :2008   Mode  :character   Mode  :character  
##  Mean   : 6.322   Mean   :2008                                        
##  3rd Qu.: 8.000   3rd Qu.:2009                                        
##  Max.   :12.000   Max.   :2010                                        
##                                                                       
##    SalePrice     
##  Min.   : 34900  
##  1st Qu.:129975  
##  Median :163000  
##  Mean   :180921  
##  3rd Qu.:214000  
##  Max.   :755000  
## 

## `geom_smooth()` using formula = 'y ~ x'

## 
## Call:
## lm(formula = SalePrice ~ GrLivArea + OverallQual + LotArea + 
##     GarageCars + KitchenQual, data = ames_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -393216  -18530    -800   17291  276909 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.002e+03  8.833e+03   0.340    0.734    
## GrLivArea      4.401e+01  2.423e+00  18.162  < 2e-16 ***
## OverallQual    2.119e+04  1.137e+03  18.637  < 2e-16 ***
## LotArea        8.313e-01  1.021e-01   8.139 8.52e-16 ***
## GarageCars     1.844e+04  1.702e+03  10.839  < 2e-16 ***
## KitchenQualFa -6.946e+04  8.027e+03  -8.652  < 2e-16 ***
## KitchenQualGd -5.492e+04  4.294e+03 -12.790  < 2e-16 ***
## KitchenQualTA -7.044e+04  4.906e+03 -14.359  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 37340 on 1452 degrees of freedom
## Multiple R-squared:  0.7802, Adjusted R-squared:  0.7791 
## F-statistic: 736.2 on 7 and 1452 DF,  p-value: < 2.2e-16

## 
## Call:
## lm(formula = SalePrice ~ GrLivArea * OverallQual + LotArea + 
##     GarageCars + KitchenQual, data = ames_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -501312  -17307    -257   16230  242184 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            7.947e+04  1.233e+04   6.447 1.55e-10 ***
## GrLivArea             -1.774e+01  7.502e+00  -2.365   0.0182 *  
## OverallQual            7.781e+03  1.903e+03   4.090 4.55e-05 ***
## LotArea                7.913e-01  9.974e-02   7.934 4.22e-15 ***
## GarageCars             1.912e+04  1.661e+03  11.508  < 2e-16 ***
## KitchenQualFa         -6.396e+04  7.855e+03  -8.142 8.30e-16 ***
## KitchenQualGd         -4.398e+04  4.374e+03 -10.055  < 2e-16 ***
## KitchenQualTA         -6.004e+04  4.933e+03 -12.173  < 2e-16 ***
## GrLivArea:OverallQual  9.134e+00  1.053e+00   8.674  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 36420 on 1451 degrees of freedom
## Multiple R-squared:  0.791,  Adjusted R-squared:  0.7899 
## F-statistic: 686.5 on 8 and 1451 DF,  p-value: < 2.2e-16

## PRINCIPAL COMPONENT ANALYSIS

## Importance of components:
##                           PC1    PC2    PC3     PC4
## Standard deviation     1.4783 0.9758 0.7208 0.58540
## Proportion of Variance 0.5464 0.2381 0.1299 0.08567
## Cumulative Proportion  0.5464 0.7844 0.9143 1.00000

1. High Predictive Power: The model strongly predicts home sale prices, explaining about 79% of the price variation adjusted R² = 0.79. This indicates that key factors like size, quality, lot dimensions, and specific features are well-represented and influential in determining prices in the Ames dataset.

2. Key Drivers of Sale Price: Five main factors significantly impact housing prices: Overall Quality strong positive effect, Lot Area (smaller positive effect), Garage Capacity (positive increase per car space), and Kitchen Quality (lower quality has a substantial negative impact). The main effect of Above Grade Living Area appears negative but is influenced by its interaction with Overall Quality.

1. The Interaction Between GrLivArea and OverallQual is a key finding is the significant interaction between living area and overall quality. More living space benefits higher quality homes significantly, while it may not increase or even decrease the value of lower quality homes. Luxury homes gain more value from added space than lower-tier properties.

2. Practical Implications: Homeowners/sellers should prioritize quality improvements, as they both directly increase price and enhance the value of added space. Buyers/agents should closely evaluate home quality alongside size. For policy/analysis, the model highlights that comprehensive upgrades drive value, with the size-quality interaction crucial for understanding market dynamics.