Usama_Shaikh_Data_Dive_Week11
2024-11-12
```{r setup, include=FALSE} knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
Loading Necessary Libraries
library(tidyverse)## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr 1.1.4 ✔ readr 2.1.5
## ✔ forcats 1.0.0 ✔ stringr 1.5.1
## ✔ ggplot2 3.5.1 ✔ tibble 3.2.1
## ✔ lubridate 1.9.3 ✔ tidyr 1.3.1
## ✔ 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 errorslibrary(broom)
library(car) # For VIF calculations## Loading required package: carData
##
## Attaching package: 'car'
##
## The following object is masked from 'package:dplyr':
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## recode
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## The following object is masked from 'package:purrr':
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## someLoading and Exploring Data
# Load the Ames dataset
ames <- read.csv('D:/Stats for DS/ames.csv', header = TRUE)
# View the structure and summary of the dataset
glimpse(ames)## Rows: 2,930
## Columns: 82
## $ Order <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,…
## $ PID <int> 526301100, 526350040, 526351010, 526353030, 527105010,…
## $ MS.SubClass <int> 20, 20, 20, 20, 60, 60, 120, 120, 120, 60, 60, 20, 60,…
## $ MS.Zoning <chr> "RL", "RH", "RL", "RL", "RL", "RL", "RL", "RL", "RL", …
## $ Lot.Frontage <int> 141, 80, 81, 93, 74, 78, 41, 43, 39, 60, 75, NA, 63, 8…
## $ Lot.Area <int> 31770, 11622, 14267, 11160, 13830, 9978, 4920, 5005, 5…
## $ 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…
## $ Lot.Shape <chr> "IR1", "Reg", "IR1", "Reg", "IR1", "IR1", "Reg", "IR1"…
## $ Land.Contour <chr> "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "Lvl", "HLS"…
## $ Utilities <chr> "AllPub", "AllPub", "AllPub", "AllPub", "AllPub", "All…
## $ Lot.Config <chr> "Corner", "Inside", "Corner", "Corner", "Inside", "Ins…
## $ Land.Slope <chr> "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl", "Gtl"…
## $ Neighborhood <chr> "NAmes", "NAmes", "NAmes", "NAmes", "Gilbert", "Gilber…
## $ Condition.1 <chr> "Norm", "Feedr", "Norm", "Norm", "Norm", "Norm", "Norm…
## $ Condition.2 <chr> "Norm", "Norm", "Norm", "Norm", "Norm", "Norm", "Norm"…
## $ Bldg.Type <chr> "1Fam", "1Fam", "1Fam", "1Fam", "1Fam", "1Fam", "Twnhs…
## $ House.Style <chr> "1Story", "1Story", "1Story", "1Story", "2Story", "2St…
## $ Overall.Qual <int> 6, 5, 6, 7, 5, 6, 8, 8, 8, 7, 6, 6, 6, 7, 8, 8, 8, 9, …
## $ Overall.Cond <int> 5, 6, 6, 5, 5, 6, 5, 5, 5, 5, 5, 7, 5, 5, 5, 5, 7, 2, …
## $ Year.Built <int> 1960, 1961, 1958, 1968, 1997, 1998, 2001, 1992, 1995, …
## $ Year.Remod.Add <int> 1960, 1961, 1958, 1968, 1998, 1998, 2001, 1992, 1996, …
## $ Roof.Style <chr> "Hip", "Gable", "Hip", "Hip", "Gable", "Gable", "Gable…
## $ Roof.Matl <chr> "CompShg", "CompShg", "CompShg", "CompShg", "CompShg",…
## $ Exterior.1st <chr> "BrkFace", "VinylSd", "Wd Sdng", "BrkFace", "VinylSd",…
## $ Exterior.2nd <chr> "Plywood", "VinylSd", "Wd Sdng", "BrkFace", "VinylSd",…
## $ Mas.Vnr.Type <chr> "Stone", "None", "BrkFace", "None", "None", "BrkFace",…
## $ Mas.Vnr.Area <int> 112, 0, 108, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 603,…
## $ Exter.Qual <chr> "TA", "TA", "TA", "Gd", "TA", "TA", "Gd", "Gd", "Gd", …
## $ Exter.Cond <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", …
## $ Foundation <chr> "CBlock", "CBlock", "CBlock", "CBlock", "PConc", "PCon…
## $ Bsmt.Qual <chr> "TA", "TA", "TA", "TA", "Gd", "TA", "Gd", "Gd", "Gd", …
## $ Bsmt.Cond <chr> "Gd", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", …
## $ Bsmt.Exposure <chr> "Gd", "No", "No", "No", "No", "No", "Mn", "No", "No", …
## $ BsmtFin.Type.1 <chr> "BLQ", "Rec", "ALQ", "ALQ", "GLQ", "GLQ", "GLQ", "ALQ"…
## $ BsmtFin.SF.1 <int> 639, 468, 923, 1065, 791, 602, 616, 263, 1180, 0, 0, 9…
## $ BsmtFin.Type.2 <chr> "Unf", "LwQ", "Unf", "Unf", "Unf", "Unf", "Unf", "Unf"…
## $ BsmtFin.SF.2 <int> 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1120, 0, 0…
## $ Bsmt.Unf.SF <int> 441, 270, 406, 1045, 137, 324, 722, 1017, 415, 994, 76…
## $ Total.Bsmt.SF <int> 1080, 882, 1329, 2110, 928, 926, 1338, 1280, 1595, 994…
## $ Heating <chr> "GasA", "GasA", "GasA", "GasA", "GasA", "GasA", "GasA"…
## $ Heating.QC <chr> "Fa", "TA", "TA", "Ex", "Gd", "Ex", "Ex", "Ex", "Ex", …
## $ Central.Air <chr> "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y",…
## $ Electrical <chr> "SBrkr", "SBrkr", "SBrkr", "SBrkr", "SBrkr", "SBrkr", …
## $ X1st.Flr.SF <int> 1656, 896, 1329, 2110, 928, 926, 1338, 1280, 1616, 102…
## $ X2nd.Flr.SF <int> 0, 0, 0, 0, 701, 678, 0, 0, 0, 776, 892, 0, 676, 0, 0,…
## $ Low.Qual.Fin.SF <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ Gr.Liv.Area <int> 1656, 896, 1329, 2110, 1629, 1604, 1338, 1280, 1616, 1…
## $ Bsmt.Full.Bath <int> 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, …
## $ Bsmt.Half.Bath <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ Full.Bath <int> 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 3, 2, 1, …
## $ Half.Bath <int> 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, …
## $ Bedroom.AbvGr <int> 3, 2, 3, 3, 3, 3, 2, 2, 2, 3, 3, 3, 3, 2, 1, 4, 4, 1, …
## $ Kitchen.AbvGr <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
## $ Kitchen.Qual <chr> "TA", "TA", "Gd", "Ex", "TA", "Gd", "Gd", "Gd", "Gd", …
## $ TotRms.AbvGrd <int> 7, 5, 6, 8, 6, 7, 6, 5, 5, 7, 7, 6, 7, 5, 4, 12, 8, 8,…
## $ Functional <chr> "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", "Typ", "Typ"…
## $ Fireplaces <int> 2, 0, 0, 2, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, …
## $ Fireplace.Qu <chr> "Gd", NA, NA, "TA", "TA", "Gd", NA, NA, "TA", "TA", "T…
## $ Garage.Type <chr> "Attchd", "Attchd", "Attchd", "Attchd", "Attchd", "Att…
## $ Garage.Yr.Blt <int> 1960, 1961, 1958, 1968, 1997, 1998, 2001, 1992, 1995, …
## $ Garage.Finish <chr> "Fin", "Unf", "Unf", "Fin", "Fin", "Fin", "Fin", "RFn"…
## $ Garage.Cars <int> 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 3, …
## $ Garage.Area <int> 528, 730, 312, 522, 482, 470, 582, 506, 608, 442, 440,…
## $ Garage.Qual <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", …
## $ Garage.Cond <chr> "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", "TA", …
## $ Paved.Drive <chr> "P", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y", "Y",…
## $ Wood.Deck.SF <int> 210, 140, 393, 0, 212, 360, 0, 0, 237, 140, 157, 483, …
## $ Open.Porch.SF <int> 62, 0, 36, 0, 34, 36, 0, 82, 152, 60, 84, 21, 75, 0, 5…
## $ Enclosed.Porch <int> 0, 0, 0, 0, 0, 0, 170, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
## $ X3Ssn.Porch <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ Screen.Porch <int> 0, 120, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 140, 210…
## $ Pool.Area <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, …
## $ Pool.QC <chr> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA…
## $ Fence <chr> NA, "MnPrv", NA, NA, "MnPrv", NA, NA, NA, NA, NA, NA, …
## $ Misc.Feature <chr> NA, NA, "Gar2", NA, NA, NA, NA, NA, NA, NA, NA, "Shed"…
## $ Misc.Val <int> 0, 0, 12500, 0, 0, 0, 0, 0, 0, 0, 0, 500, 0, 0, 0, 0, …
## $ Mo.Sold <int> 5, 6, 6, 4, 3, 6, 4, 1, 3, 6, 4, 3, 5, 2, 6, 6, 6, 6, …
## $ Yr.Sold <int> 2010, 2010, 2010, 2010, 2010, 2010, 2010, 2010, 2010, …
## $ Sale.Type <chr> "WD ", "WD ", "WD ", "WD ", "WD ", "WD ", "WD ", "WD "…
## $ Sale.Condition <chr> "Normal", "Normal", "Normal", "Normal", "Normal", "Nor…
## $ SalePrice <int> 215000, 105000, 172000, 244000, 189900, 195500, 213500…summary(ames)## Order PID MS.SubClass MS.Zoning
## Min. : 1.0 Min. :5.263e+08 Min. : 20.00 Length:2930
## 1st Qu.: 733.2 1st Qu.:5.285e+08 1st Qu.: 20.00 Class :character
## Median :1465.5 Median :5.355e+08 Median : 50.00 Mode :character
## Mean :1465.5 Mean :7.145e+08 Mean : 57.39
## 3rd Qu.:2197.8 3rd Qu.:9.072e+08 3rd Qu.: 70.00
## Max. :2930.0 Max. :1.007e+09 Max. :190.00
##
## Lot.Frontage Lot.Area Street Alley
## Min. : 21.00 Min. : 1300 Length:2930 Length:2930
## 1st Qu.: 58.00 1st Qu.: 7440 Class :character Class :character
## Median : 68.00 Median : 9436 Mode :character Mode :character
## Mean : 69.22 Mean : 10148
## 3rd Qu.: 80.00 3rd Qu.: 11555
## Max. :313.00 Max. :215245
## NA's :490
## Lot.Shape Land.Contour Utilities Lot.Config
## Length:2930 Length:2930 Length:2930 Length:2930
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Land.Slope Neighborhood Condition.1 Condition.2
## Length:2930 Length:2930 Length:2930 Length:2930
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Bldg.Type House.Style Overall.Qual Overall.Cond
## Length:2930 Length:2930 Min. : 1.000 Min. :1.000
## Class :character Class :character 1st Qu.: 5.000 1st Qu.:5.000
## Mode :character Mode :character Median : 6.000 Median :5.000
## Mean : 6.095 Mean :5.563
## 3rd Qu.: 7.000 3rd Qu.:6.000
## Max. :10.000 Max. :9.000
##
## Year.Built Year.Remod.Add Roof.Style Roof.Matl
## Min. :1872 Min. :1950 Length:2930 Length:2930
## 1st Qu.:1954 1st Qu.:1965 Class :character Class :character
## Median :1973 Median :1993 Mode :character Mode :character
## Mean :1971 Mean :1984
## 3rd Qu.:2001 3rd Qu.:2004
## Max. :2010 Max. :2010
##
## Exterior.1st Exterior.2nd Mas.Vnr.Type Mas.Vnr.Area
## Length:2930 Length:2930 Length:2930 Min. : 0.0
## Class :character Class :character Class :character 1st Qu.: 0.0
## Mode :character Mode :character Mode :character Median : 0.0
## Mean : 101.9
## 3rd Qu.: 164.0
## Max. :1600.0
## NA's :23
## Exter.Qual Exter.Cond Foundation Bsmt.Qual
## Length:2930 Length:2930 Length:2930 Length:2930
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## Bsmt.Cond Bsmt.Exposure BsmtFin.Type.1 BsmtFin.SF.1
## Length:2930 Length:2930 Length:2930 Min. : 0.0
## Class :character Class :character Class :character 1st Qu.: 0.0
## Mode :character Mode :character Mode :character Median : 370.0
## Mean : 442.6
## 3rd Qu.: 734.0
## Max. :5644.0
## NA's :1
## BsmtFin.Type.2 BsmtFin.SF.2 Bsmt.Unf.SF Total.Bsmt.SF
## Length:2930 Min. : 0.00 Min. : 0.0 Min. : 0
## Class :character 1st Qu.: 0.00 1st Qu.: 219.0 1st Qu.: 793
## Mode :character Median : 0.00 Median : 466.0 Median : 990
## Mean : 49.72 Mean : 559.3 Mean :1052
## 3rd Qu.: 0.00 3rd Qu.: 802.0 3rd Qu.:1302
## Max. :1526.00 Max. :2336.0 Max. :6110
## NA's :1 NA's :1 NA's :1
## Heating Heating.QC Central.Air Electrical
## Length:2930 Length:2930 Length:2930 Length:2930
## Class :character Class :character Class :character Class :character
## Mode :character Mode :character Mode :character Mode :character
##
##
##
##
## X1st.Flr.SF X2nd.Flr.SF Low.Qual.Fin.SF Gr.Liv.Area
## Min. : 334.0 Min. : 0.0 Min. : 0.000 Min. : 334
## 1st Qu.: 876.2 1st Qu.: 0.0 1st Qu.: 0.000 1st Qu.:1126
## Median :1084.0 Median : 0.0 Median : 0.000 Median :1442
## Mean :1159.6 Mean : 335.5 Mean : 4.677 Mean :1500
## 3rd Qu.:1384.0 3rd Qu.: 703.8 3rd Qu.: 0.000 3rd Qu.:1743
## Max. :5095.0 Max. :2065.0 Max. :1064.000 Max. :5642
##
## Bsmt.Full.Bath Bsmt.Half.Bath Full.Bath Half.Bath
## Min. :0.0000 Min. :0.00000 Min. :0.000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:1.000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :2.000 Median :0.0000
## Mean :0.4314 Mean :0.06113 Mean :1.567 Mean :0.3795
## 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.:2.000 3rd Qu.:1.0000
## Max. :3.0000 Max. :2.00000 Max. :4.000 Max. :2.0000
## NA's :2 NA's :2
## Bedroom.AbvGr Kitchen.AbvGr Kitchen.Qual TotRms.AbvGrd
## Min. :0.000 Min. :0.000 Length:2930 Min. : 2.000
## 1st Qu.:2.000 1st Qu.:1.000 Class :character 1st Qu.: 5.000
## Median :3.000 Median :1.000 Mode :character Median : 6.000
## Mean :2.854 Mean :1.044 Mean : 6.443
## 3rd Qu.:3.000 3rd Qu.:1.000 3rd Qu.: 7.000
## Max. :8.000 Max. :3.000 Max. :15.000
##
## Functional Fireplaces Fireplace.Qu Garage.Type
## Length:2930 Min. :0.0000 Length:2930 Length:2930
## Class :character 1st Qu.:0.0000 Class :character Class :character
## Mode :character Median :1.0000 Mode :character Mode :character
## Mean :0.5993
## 3rd Qu.:1.0000
## Max. :4.0000
##
## Garage.Yr.Blt Garage.Finish Garage.Cars Garage.Area
## Min. :1895 Length:2930 Min. :0.000 Min. : 0.0
## 1st Qu.:1960 Class :character 1st Qu.:1.000 1st Qu.: 320.0
## Median :1979 Mode :character Median :2.000 Median : 480.0
## Mean :1978 Mean :1.767 Mean : 472.8
## 3rd Qu.:2002 3rd Qu.:2.000 3rd Qu.: 576.0
## Max. :2207 Max. :5.000 Max. :1488.0
## NA's :159 NA's :1 NA's :1
## Garage.Qual Garage.Cond Paved.Drive Wood.Deck.SF
## Length:2930 Length:2930 Length:2930 Min. : 0.00
## Class :character Class :character Class :character 1st Qu.: 0.00
## Mode :character Mode :character Mode :character Median : 0.00
## Mean : 93.75
## 3rd Qu.: 168.00
## Max. :1424.00
##
## Open.Porch.SF Enclosed.Porch X3Ssn.Porch Screen.Porch
## Min. : 0.00 Min. : 0.00 Min. : 0.000 Min. : 0
## 1st Qu.: 0.00 1st Qu.: 0.00 1st Qu.: 0.000 1st Qu.: 0
## Median : 27.00 Median : 0.00 Median : 0.000 Median : 0
## Mean : 47.53 Mean : 23.01 Mean : 2.592 Mean : 16
## 3rd Qu.: 70.00 3rd Qu.: 0.00 3rd Qu.: 0.000 3rd Qu.: 0
## Max. :742.00 Max. :1012.00 Max. :508.000 Max. :576
##
## Pool.Area Pool.QC Fence Misc.Feature
## Min. : 0.000 Length:2930 Length:2930 Length:2930
## 1st Qu.: 0.000 Class :character Class :character Class :character
## Median : 0.000 Mode :character Mode :character Mode :character
## Mean : 2.243
## 3rd Qu.: 0.000
## Max. :800.000
##
## Misc.Val Mo.Sold Yr.Sold Sale.Type
## Min. : 0.00 Min. : 1.000 Min. :2006 Length:2930
## 1st Qu.: 0.00 1st Qu.: 4.000 1st Qu.:2007 Class :character
## Median : 0.00 Median : 6.000 Median :2008 Mode :character
## Mean : 50.63 Mean : 6.216 Mean :2008
## 3rd Qu.: 0.00 3rd Qu.: 8.000 3rd Qu.:2009
## Max. :17000.00 Max. :12.000 Max. :2010
##
## Sale.Condition SalePrice
## Length:2930 Min. : 12789
## Class :character 1st Qu.:129500
## Mode :character Median :160000
## Mean :180796
## 3rd Qu.:213500
## Max. :755000
## # Convert Central.Air to binary for logistic regression
ames <- ames %>% mutate(Central.Air = ifelse(Central.Air == "Y", 1, 0))Model Building
# Fit the linear model
linear_model <- lm(SalePrice ~ Gr.Liv.Area + Lot.Area + Overall.Qual, data = ames)
# Summary of the linear model
summary(linear_model)##
## Call:
## lm(formula = SalePrice ~ Gr.Liv.Area + Lot.Area + Overall.Qual,
## data = ames)
##
## Residuals:
## Min 1Q Median 3Q Max
## -432835 -22651 -1106 19280 283790
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.162e+05 3.390e+03 -34.28 <2e-16 ***
## Gr.Liv.Area 5.265e+01 1.877e+00 28.05 <2e-16 ***
## Lot.Area 1.148e+00 9.934e-02 11.56 <2e-16 ***
## Overall.Qual 3.387e+04 6.474e+02 52.31 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 40460 on 2926 degrees of freedom
## Multiple R-squared: 0.7437, Adjusted R-squared: 0.7435
## F-statistic: 2831 on 3 and 2926 DF, p-value: < 2.2e-16Logistic Regression Model
# Prepare data for logistic regression
ames_model_data <- ames %>% select(Central.Air, Gr.Liv.Area, Overall.Qual, Year.Built, Lot.Area) %>% na.omit()
# Fit the logistic regression model
logit_model <- glm(Central.Air ~ Gr.Liv.Area + Overall.Qual + Year.Built + Lot.Area,
data = ames_model_data, family = binomial(link = "logit"))
# Summary of the logistic regression model
summary(logit_model)##
## Call:
## glm(formula = Central.Air ~ Gr.Liv.Area + Overall.Qual + Year.Built +
## Lot.Area, family = binomial(link = "logit"), data = ames_model_data)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -9.668e+01 7.345e+00 -13.162 < 2e-16 ***
## Gr.Liv.Area 2.246e-04 2.333e-04 0.963 0.3357
## Overall.Qual 7.117e-01 8.922e-02 7.976 1.51e-15 ***
## Year.Built 4.870e-02 3.779e-03 12.888 < 2e-16 ***
## Lot.Area 3.727e-05 2.195e-05 1.698 0.0894 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for binomial family taken to be 1)
##
## Null deviance: 1438.81 on 2929 degrees of freedom
## Residual deviance: 943.58 on 2925 degrees of freedom
## AIC: 953.58
##
## Number of Fisher Scoring iterations: 7Model Diagnostics
Residual Plot: Checking for patterns to detect heteroscedasticity or model misfit.
Q-Q Plot: Assessing the normality of residuals.
# Residuals vs Fitted
plot(linear_model, which = 1)
# Normal Q-Q plot
plot(linear_model, which = 2)
- Multicollinearity Check: Calculating VIF to assess potential multicollinearity issues.
vif(linear_model)## Gr.Liv.Area Lot.Area Overall.Qual
## 1.610324 1.096466 1.493078Logistic Regression Diagnostics
AIC: Using AIC to assess the model fit.
Odds Ratios for Interpretation.
# AIC of logistic model
AIC(logit_model)## [1] 953.5784# Convert coefficients to odds ratios
exp(coef(logit_model))## (Intercept) Gr.Liv.Area Overall.Qual Year.Built Lot.Area
## 1.029973e-42 1.000225e+00 2.037369e+00 1.049906e+00 1.000037e+00Interpretation of Coefficients
Linear Model Coefficient Interpretation
The coefficient for Gr.Liv.Area in the linear model can be interpreted as the increase in SalePrice for each additional unit of living area, holding other factors constant.
# Extracting coefficients with confidence intervals
tidy(linear_model, conf.int = TRUE)## # A tibble: 4 × 7
## term estimate std.error statistic p.value conf.low conf.high
## <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 (Intercept) -116223. 3390. -34.3 7.88e-217 -122870. -109576.
## 2 Gr.Liv.Area 52.6 1.88 28.1 1.48e-153 49.0 56.3
## 3 Lot.Area 1.15 0.0993 11.6 2.99e- 30 0.954 1.34
## 4 Overall.Qual 33867. 647. 52.3 0 32597. 35136.Logistic Regression Coefficient Interpretation
For the logistic model, we interpret the odds ratios to understand how the probability of having central air changes with each predictor.
# Confidence interval for Gr.Liv.Area in logistic model
coeff_se <- summary(logit_model)$coefficients["Gr.Liv.Area", "Std. Error"]
coeff <- coef(logit_model)["Gr.Liv.Area"]
z_value <- 1.96
ci_lower <- coeff - z_value * coeff_se
ci_upper <- coeff + z_value * coeff_se
ci <- c(ci_lower, ci_upper)
exp(ci)## Gr.Liv.Area Gr.Liv.Area
## 0.9997674 1.0006820Insights and Further Investigations
1. Linear Model Analysis (SalePrice)
Model Performance
R-squared: 0.7437 (74.37% of variance explained)
F-statistic: 2831 (p < 2.2e-16)
Highly significant overall model fit
Coefficient Interpretation
Gr.Liv.Area: β = 52.65 (SE = 1.88)
For each square foot increase in living area
Price increases by approximately $52.65
Highly significant (p < 2e-16)
Lot.Area: β = 1.15 (SE = 0.099)
Each square foot of lot area
Adds approximately $1.15 to price
Highly significant (p < 2e-16)
Overall.Qual: β = 33,867 (SE = 647.41)
Each point increase in overall quality
Adds approximately $33,867 to price
Strongest predictor in terms of magnitude
Diagnostic Issues
Residuals Plot Issues:
Shows fan pattern (heteroscedasticity)
Wider spread of residuals at higher fitted values
Several notable outliers (especially 1499, 2181, 2182)
Suggests potential need for transformation
Q-Q Plot Concerns:
Heavy tails at both ends
Deviation from normality especially pronounced in lower tail
Suggests non-normal residuals
Multicollinearity Assessment:
VIF values all below 2 (Gr.Liv.Area: 1.61, Lot.Area: 1.10, Overall.Qual: 1.49)
No concerning multicollinearity detected
2. Logistic Model Analysis (Central Air)
Model Performance
AIC: 953.58
Null deviance: 1438.81 → Residual deviance: 943.58
Significant reduction in deviance indicates good model fit
Odds Ratio Interpretation
Overall.Qual: OR = 2.037
Each unit increase in quality
Doubles the odds of having central air
Highly significant (p < 1.51e-15)
Year.Built: OR = 1.050
Each year newer
Increases odds by 5%
Highly significant (p < 2e-16)
Gr.Liv.Area: OR = 1.0002
Minimal effect
Not statistically significant (p = 0.336)
CI: [0.9998, 1.0007] includes 1
Lot.Area: OR = 1.000037
- Negligible effect
- Marginally significant (p = 0.0894)Key Insights
Model Selection and Specification:
Linear model shows good predictive power but violates assumptions
Logistic model effectively predicts central air presence
Both models identify Overall.Qual as crucial predictor
Variable Importance:
Overall.Qual significant in both models
Year.Built crucial for central air
Living area more important for price than central air
Data Structure:
Price relationships are non-linear
Central air relationships are more straightforward
Some influential outliers present
Further Investigations
Model Improvements:
Consider log transformation of SalePrice
Investigate influential outliers (esp. 1499, 2181, 2182)
Test for interaction effects
Additional Analysis:
Examine residual patterns by year built
Study relationship between price and central air
Investigate neighborhood effects
Variable Transformations:
Test polynomial terms for Overall.Qual
Consider standardizing lot and living areas
Explore binning of continuous variables