DSC-Assignment6.1
library(“readxl”)
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When you click the Knit button a document will be generated that includes both content as well as the output of any embedded R code chunks within the document. You can embed an R code chunk like this: setwd(“C:/Users/Owner/Desktop/Lenin Files/Data Sciences”) # copy and load home sales data
##setwd("C:/Users/Owner/Desktop/Lenin Files/Data Sciences")
homesales<- read.csv(file = "C:/Users/Owner/Desktop/Lenin Files/Data Sciences/week-6-housing.csv", header=TRUE)check data
summary(homesales)## Sale.Date Sale.Price sale_reason sale_instrument
## 7/1/2008 : 41 Min. : 698 Min. : 0.00 Min. : 0.000
## 10/1/2008 : 38 1st Qu.: 460000 1st Qu.: 1.00 1st Qu.: 3.000
## 11/17/2011: 33 Median : 593000 Median : 1.00 Median : 3.000
## 10/2/2012 : 22 Mean : 660738 Mean : 1.55 Mean : 3.678
## 5/17/2010 : 17 3rd Qu.: 750000 3rd Qu.: 1.00 3rd Qu.: 3.000
## 9/13/2011 : 16 Max. :4400000 Max. :19.00 Max. :27.000
## (Other) :12698
## sale_warning sitetype addr_full zip5
## :10568 A1: 8 22340 NE 65TH PL : 6 Min. :98052
## 45 : 257 C1: 3 23566 NE 111TH ST : 6 1st Qu.:98052
## 54 : 202 DV: 6 9102 172ND AVE NE : 6 Median :98052
## 40 : 177 R1:12456 10920 167TH AVE NE : 5 Mean :98053
## 41 : 175 R2: 377 11093 ELLISTON WAY NE: 5 3rd Qu.:98053
## 15 : 149 R3: 14 15604 NE 112TH ST : 5 Max. :98074
## (Other): 1337 R4: 1 (Other) :12832
## ctyname postalctyn lon lat
## :6078 REDMOND:12865 Min. :-122.2 Min. :47.46
## REDMOND :6721 1st Qu.:-122.1 1st Qu.:47.67
## SAMMAMISH: 66 Median :-122.1 Median :47.69
## Mean :-122.1 Mean :47.68
## 3rd Qu.:-122.0 3rd Qu.:47.70
## Max. :-121.9 Max. :47.73
##
## building_grade square_feet_total_living bedrooms
## Min. : 2.00 Min. : 240 Min. : 0.000
## 1st Qu.: 8.00 1st Qu.: 1820 1st Qu.: 3.000
## Median : 8.00 Median : 2420 Median : 4.000
## Mean : 8.24 Mean : 2540 Mean : 3.479
## 3rd Qu.: 9.00 3rd Qu.: 3110 3rd Qu.: 4.000
## Max. :13.00 Max. :13540 Max. :11.000
##
## bath_full_count bath_half_count bath_3qtr_count year_built
## Min. : 0.000 Min. :0.0000 Min. :0.000 Min. :1900
## 1st Qu.: 1.000 1st Qu.:0.0000 1st Qu.:0.000 1st Qu.:1979
## Median : 2.000 Median :1.0000 Median :0.000 Median :1998
## Mean : 1.798 Mean :0.6134 Mean :0.494 Mean :1993
## 3rd Qu.: 2.000 3rd Qu.:1.0000 3rd Qu.:1.000 3rd Qu.:2007
## Max. :23.000 Max. :8.0000 Max. :8.000 Max. :2016
##
## year_renovated current_zoning sq_ft_lot prop_type
## Min. : 0.00 URPSO :3215 Min. : 785 R:12865
## 1st Qu.: 0.00 R4 :2893 1st Qu.: 5355
## Median : 0.00 RA5 :1974 Median : 7965
## Mean : 26.24 R5 :1933 Mean : 22229
## 3rd Qu.: 0.00 R6 :1456 3rd Qu.: 12632
## Max. :2016.00 R3 : 331 Max. :1631322
## (Other):1063
## present_use
## Min. : 0.000
## 1st Qu.: 2.000
## Median : 2.000
## Mean : 6.598
## 3rd Qu.: 2.000
## Max. :300.000
## b. created the following variables 1) Sale price and 2)Square feet of lot 3) Square feet of living area 4) year built.
salePrice1 <- homesales$Sale.Price
sqFoot <- homesales$sq_ft_lot
yearBuilt <- homesales$year_built
sqFootLiving <- homesales$square_feet_total_livingbuild a model where sale price is predicted from square foot of the lot
homesales1 <- lm(salePrice1 ~ sqFoot, data = homesales)
summary(homesales1)##
## Call:
## lm(formula = salePrice1 ~ sqFoot, data = homesales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2016064 -194842 -63293 91565 3735109
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.418e+05 3.800e+03 168.90 <2e-16 ***
## sqFoot 8.510e-01 6.217e-02 13.69 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 401500 on 12863 degrees of freedom
## Multiple R-squared: 0.01435, Adjusted R-squared: 0.01428
## F-statistic: 187.3 on 1 and 12863 DF, p-value: < 2.2e-16build a model where sale price is predicted from square feet of the lot, square feet of living area and year built
homesales2 <- lm(salePrice1 ~ sqFoot + yearBuilt + sqFootLiving, data = homesales)
summary(homesales2)##
## Call:
## lm(formula = salePrice1 ~ sqFoot + yearBuilt + sqFootLiving,
## data = homesales)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2158828 -119944 -41323 46104 3761175
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -5.547e+06 3.901e+05 -14.219 < 2e-16 ***
## sqFoot 2.924e-01 5.837e-02 5.009 5.55e-07 ***
## yearBuilt 2.900e+03 1.971e+02 14.711 < 2e-16 ***
## sqFootLiving 1.663e+02 3.495e+00 47.592 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 357200 on 12861 degrees of freedom
## Multiple R-squared: 0.22, Adjusted R-squared: 0.2198
## F-statistic: 1209 on 3 and 12861 DF, p-value: < 2.2e-16c. homesales1 modle was generated using square foot data and the value of R2 is 0.014, which means only 1.4% of the sales price is influenced by the lot footage. When I added additional variables the R2 increased to 22%. That means actual living area and year of built account for 20.6% of the variability in home sale price.
The difference in the R-squared and Adjusted R-squared in the first model is 0.07%, which indicates that if the model is derived from the population rather than a sample it would account for approximately 0.007% less variance in the outcome. This variation is negigible
when I added more predictor variables, the difference in R values increased to 0.02%.
d. the beta values in the multiple regression model are intercept=-5.547, sqfoot of lot(b1)=0.2924, year built(b2)=2900, living area(b3)=166.3. It indicates there is positive relation ship between b values and the price of the home. As all beta value increases, the price of the homes increase. Also, as the living areas increases by one foot, the value of the home increases by $166 and as year increases by one unit, the value of the home increases by $2900 when rest of the effects are held constant in each case.
Find the confidence intervals below
confint(homesales2)## 2.5 % 97.5 %
## (Intercept) -6.311551e+06 -4.782253e+06
## sqFoot 1.779547e-01 4.067827e-01
## yearBuilt 2.513176e+03 3.285875e+03
## sqFootLiving 1.594730e+02 1.731737e+02e.In regression model, the confidence interval for living area is tight (159.4 and 173.1), indicating that the estimates of the current model are likely to be representative of the true population values. Same thing is true with year built parameter.
Compare models
anova(homesales1, homesales2)## Analysis of Variance Table
##
## Model 1: salePrice1 ~ sqFoot
## Model 2: salePrice1 ~ sqFoot + yearBuilt + sqFootLiving
## Res.Df RSS Df Sum of Sq F Pr(>F)
## 1 12863 2.0734e+15
## 2 12861 1.6409e+15 2 4.3252e+14 1695 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1f. the value of F is 1695 and F(2,12861)=1695, P<2.22-16. It means the homesales2 significantly improved the fit of the model to the data compared to homesales1
g. Perform casewise dignostics and save each function’s output as a variable in a dataframe
homesales$residuals <- resid(homesales2)
homesales$standardized.residuals <- rstandard(homesales2)
homesales$studentized.residuals <- rstudent(homesales2)
homesales$dfbeta <- dfbeta(homesales2)
homesales$dffit <- dffits(homesales2)
write.table(homesales, "Home sales with Diagnostics", sep = "\t", row.names= FALSE)h. Calculate the standardized residuals specifying those that are +-2, storing the results of large residuals in a variable
i. show the sum of large residuals
homesales$large.residual <- homesales$standardized.residuals > 2 | homesales$standardized.residuals < -2
sum(homesales$large.residual)## [1] 334There are 334 cases with large residuals
j. show the variables with large residuals. Selected only a few columns
homesales[homesales$large.residual, c("Sale.Price", "addr_full", "zip5", "year_built", "square_feet_total_living" )]## Sale.Price addr_full zip5 year_built
## 6 184667 8101 229TH DR NE 98053 2005
## 25 265000 25149 NE PATTERSON WAY 98053 2007
## 115 1390000 19656 NE REDMOND RD 98053 1955
## 160 229000 28527 NE 47TH PL 98053 2008
## 178 390000 13414 WOODINVILLE REDMOND RD NE 98052 2008
## 239 1588359 24103 NE 122ND ST 98053 2005
## 246 1450000 3068 W LAKE SAMMAMISH PKWY NE 98052 1918
## 287 163000 28218 NE 40TH ST 98053 2014
## 295 270000 5806 249TH CT NE 98053 2016
## 300 200000 8015 228TH AVE NE 98053 2008
## 341 300000 11650 154TH PL NE 98052 2008
## 344 90000 1520 268TH AVE NE 98053 2003
## 359 187000 3131 269TH AVE NE 98053 2008
## 385 2500000 20424 NE 64TH PL 98053 2005
## 396 2169000 8024 255TH AVE NE 98053 2005
## 475 1534000 2454 W LAKE SAMMAMISH PKWY NE 98052 1963
## 482 555000 3624 175TH CT NE 98052 2007
## 508 65000 7717 252ND AVE NE 98053 2010
## 528 435000 2829 W LAKE SAMMAMISH PKWY NE 98052 2014
## 576 333000 25525 NE 67TH PL 98053 2008
## 661 2569000 8027 255TH AVE NE 98053 2006
## 670 2583000 2612 W LAKE SAMMAMISH PKWY NE 98052 1992
## 679 350000 24300 NE UNION HILL RD 98053 2008
## 784 325000 4224 244TH AVE NE 98053 2015
## 802 340000 4402 244TH AVE NE 98053 2008
## 811 3000000 2438 W LAKE SAMMAMISH PKWY NE 98052 2001
## 853 1595000 24629 NE 109TH ST 98053 1985
## 877 157000 8303 250TH AVE NE 98053 2008
## 916 450000 7350 259TH PL NE 98053 2007
## 1009 175000 5235 279TH AVE NE 98053 2005
## 1119 279150 7515 238TH AVE NE 98053 2007
## 1142 279150 7533 238TH AVE NE 98053 2007
## 1155 32000 8700 196TH AVE NE 98053 2007
## 1305 1316000 2458 W LAKE SAMMAMISH PKWY NE 98052 1929
## 1368 375000 27935 E MAIN ST 98053 2010
## 1380 80000 3605 289TH AVE NE 98053 2008
## 1442 1085000 3122 W AMES LAKE DR NE 98053 1954
## 1492 285000 11820 204TH AVE NE 98053 2007
## 1504 452800 25509 NE 100TH ST 98053 2008
## 1550 276450 11926 204TH AVE NE 98053 2007
## 1633 5000 8490 138TH LN NE 98052 2014
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## 1745 2235000 23812 NE 61ST ST 98053 2006
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## 1964 1600000 2030 W LAKE SAMMAMISH PKWY NE 98052 1979
## 1976 2625000 14026 NE 85TH CT 98052 2009
## 1977 2625000 14009 NE 85TH CT 98052 2009
## 1978 2625000 14007 NE 85TH CT 98052 2008
## 1979 2625000 14005 NE 85TH CT 98052 2008
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## 2709 2300000 9113 258TH AVE NE 98053 2016
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## 2717 2598000 8212 255TH AVE NE 98053 2007
## 2742 10570 5826 249TH CT NE 98053 2013
## 2852 3995000 13707 160TH AVE NE 98052 2000
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## 3837 130000 22465 NE 111TH LN 98053 2014
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## 4055 2000000 2844 W LAKE SAMMAMISH PKWY NE 98052 1991
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## 4248 1500 5106 272ND AVE NE 98053 1988
## 4285 155026 9256 225TH WAY NE 98053 2003
## 4391 125000 5920 216TH PL NE 98053 2015
## 4435 188750 15808 NE 51ST ST 98052 2011
## 4571 873 8340 196TH AVE NE 98053 1955
## 4648 4400000 12025 154TH PL NE 98052 1999
## 4649 4400000 12053 154TH PL NE 98052 1935
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## 5549 241000 8036 196TH AVE NE 98053 2013
## 5935 180000 10100 203RD AVE NE 98053 2012
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## 6449 4140203 12249 164TH CT NE 98052 2012
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## 6451 4140203 12228 164TH CT NE 98052 2012
## 6452 4140203 12250 164TH CT NE 98052 2013
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## 6457 4140203 12225 164TH CT NE 98052 2012
## 6512 2500000 3018 W LAKE SAMMAMISH PKWY NE 98052 1990
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## 6766 155000 2930 288TH AVE NE 98053 2013
## 6796 226610 17340 NE 36TH ST 98052 2014
## 6821 20000 13354 NE 80TH ST 98052 1955
## 6931 149650 8937 236TH AVE NE 98053 2004
## 6938 2300000 11516 174TH CT NE 98052 2013
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## 6940 2300000 17317 NE 116TH CT 98052 2013
## 6941 2300000 17321 NE 116TH CT 98052 2013
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## 6944 2300000 11503 174TH CT NE 98052 2013
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## 7446 3462000 10814 240TH AVE NE 98053 2013
## 7447 3462000 10818 240TH AVE NE 98053 2013
## 7448 3462000 10932 240TH AVE NE 98053 2013
## 7449 3462000 10921 EASTRIDGE DR NE 98053 2013
## 7450 3462000 10915 EASTRIDGE DR NE 98053 2013
## 7451 3462000 10821 EASTRIDGE DR NE 98053 2013
## 7452 3462000 10811 EASTRIDGE DR NE 98053 2013
## 7453 3462000 10888 240TH AVE NE 98053 2012
## 7454 3462000 10910 240TH AVE NE 98053 2012
## 7455 3462000 10918 240TH AVE NE 98053 2012
## 7456 3462000 10940 240TH AVE NE 98053 2013
## 7457 3462000 10956 240TH AVE NE 98053 2013
## 7458 3462000 10989 EASTRIDGE DR NE 98053 2013
## 7459 3462000 10945 EASTRIDGE DR NE 98053 2013
## 7460 3462000 10937 EASTRIDGE DR NE 98053 2013
## 7461 3462000 10929 EASTRIDGE DR NE 98053 2013
## 7462 3462000 10909 EASTRIDGE DR NE 98053 2013
## 7463 3462000 10815 EASTRIDGE DR NE 98053 2013
## 7507 229687 4224 244TH AVE NE 98053 2015
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## 7871 347000 25025 NE 80TH ST 98053 2015
## 8119 100000 13354 NE 80TH ST 98052 1955
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## 8232 226000 4224 244TH AVE NE 98053 2015
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## 8320 302500 11320 244TH AVE NE 98053 2016
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## 8535 245000 13304 NE 75TH ST 98052 2014
## 8541 2500 8490 138TH LN NE 98052 2014
## 8698 1700000 3040 W LAKE SAMMAMISH PKWY NE 98052 2014
## 8710 2750000 3244 W LAKE SAMMAMISH PKWY NE 98052 1996
## 8763 1650000 2608 W LAKE SAMMAMISH PKWY NE 98052 1972
## 8887 3340000 3026 W LAKE SAMMAMISH PKWY NE 98052 2008
## 8911 2160200 2006 250TH PL NE 98074 2003
## 8946 2160200 2006 250TH PL NE 98074 2003
## 9215 1401322 12210 WILLOWS RD NE 98052 1954
## 9293 425000 2829 W LAKE SAMMAMISH PKWY NE 98052 2014
## 9369 150000 2722 288TH AVE NE 98053 2015
## 9420 320000 22614 NE UNION HILL RD 98053 2015
## 9453 299500 22340 NE 65TH PL 98053 2015
## 9528 8000 20338 NE 85TH ST 98053 2006
## 9546 150000 22465 NE 111TH LN 98053 2014
## 9722 1700000 2850 W LAKE SAMMAMISH PKWY NE 98052 1974
## 10125 2200000 20015 NE 85TH ST 98053 1998
## 10318 2140000 8565 261ST AVE NE 98053 1997
## 10371 299000 22016 NE REDMOND FALL CITY RD 98053 2016
## 10418 325000 19841 NE REDMOND RD 98053 2003
## 10623 321000 25621 NE 42ND PL 98053 2016
## 10707 1442500 16410 NE 43RD CT 98052 1987
## 10723 1850000 15339 NE 106TH CT 98052 2008
## 10741 285000 6228 224TH AVE NE 98053 2015
## 10787 2200000 3230 W LAKE SAMMAMISH PKWY NE 98052 1952
## 10844 1200000 15430 NE 51ST ST 98052 1918
## 10958 18000 24143 NE 58TH PL 98053 1997
## 10995 1050000 8513 255TH AVE NE 98053 2005
## 11165 1890000 2410 W LAKE SAMMAMISH PKWY NE 98052 1995
## 11289 2300000 3260 W LAKE SAMMAMISH PKWY NE 98052 1982
## 11413 2025000 8071 208TH AVE NE 98053 1948
## 11558 2150000 11004 132ND AVE NE 98052 1952
## 11586 1700000 2864 W LAKE SAMMAMISH PKWY NE 98052 1938
## 11728 1840000 21031 NE 122ND ST 98053 1981
## 11758 269000 22016 NE REDMOND FALL CITY RD 98053 2016
## 11772 3750000 2808 W LAKE SAMMAMISH PKWY NE 98052 2001
## 11822 2850000 2420 W LAKE SAMMAMISH PKWY NE 98052 2005
## 11898 2165000 11207 248TH AVE NE 98053 1999
## 11899 2165000 11207 248TH AVE NE 98053 1999
## 11982 3175000 7350 259TH PL NE 98053 2007
## 11992 4311000 17656 NE 116TH ST 98052 1964
## 12212 1200000 25205 NE 80TH ST 98053 1932
## 12255 1730000 19610 NE 116TH ST 98053 1980
## 12256 1730000 19610 NE 116TH ST 98053 1980
## 12392 1450000 11220 196TH AVE NE 98053 1987
## 12472 2350000 3020 W LAKE SAMMAMISH PKWY NE 98052 1955
## 12487 2200000 2656 W LAKE SAMMAMISH PKWY NE 98052 1962
## 12577 2700000 7702 196TH AVE NE 98053 2005
## 12582 3950000 2942 W LAKE SAMMAMISH PKWY NE 98052 1974
## 12643 3850000 7917 219TH AVE NE 98053 2009
## 12686 148200 3851 E AMES LAKE DR NE 98053 2006
## 12759 1700000 13301 180TH AVE NE 98052 1990
## 12764 2988000 18025 NE 136TH ST 98052 2006
## square_feet_total_living
## 6 4160
## 25 4920
## 115 660
## 160 3840
## 178 5800
## 239 3360
## 246 900
## 287 4710
## 295 5060
## 300 6880
## 341 4490
## 344 2700
## 359 5140
## 385 6310
## 396 5080
## 475 3320
## 482 6380
## 508 3700
## 528 5830
## 576 4320
## 661 8090
## 670 4710
## 679 8490
## 784 5150
## 802 4380
## 811 5270
## 853 3470
## 877 4640
## 916 7640
## 1009 4040
## 1119 6340
## 1142 5980
## 1155 4740
## 1305 2800
## 1368 4550
## 1380 3660
## 1442 340
## 1492 4610
## 1504 7780
## 1550 5380
## 1633 3130
## 1650 9360
## 1716 4610
## 1745 5360
## 1870 10630
## 1962 5300
## 1963 3090
## 1964 550
## 1976 3830
## 1977 3330
## 1978 3480
## 1979 3370
## 1980 3350
## 1981 4080
## 1982 3690
## 2022 900
## 2099 5020
## 2137 2820
## 2157 3130
## 2257 2940
## 2264 1540
## 2302 6340
## 2360 3200
## 2361 310
## 2469 2980
## 2604 3060
## 2684 3410
## 2685 3660
## 2686 4500
## 2687 3480
## 2688 3310
## 2689 4340
## 2690 4390
## 2699 5270
## 2708 4710
## 2709 5100
## 2710 4910
## 2717 5390
## 2742 3950
## 2852 11810
## 2867 5400
## 2934 4610
## 2937 4610
## 3097 5320
## 3102 4790
## 3110 1290
## 3111 1920
## 3168 1290
## 3169 1290
## 3170 1600
## 3171 1740
## 3172 1710
## 3173 1740
## 3174 1710
## 3175 1460
## 3176 1820
## 3177 1840
## 3178 1840
## 3179 1600
## 3180 1840
## 3181 1600
## 3182 1290
## 3183 1290
## 3184 1290
## 3185 1290
## 3186 1290
## 3187 1290
## 3188 1290
## 3189 1460
## 3190 1710
## 3191 1460
## 3192 1740
## 3193 1710
## 3194 1710
## 3195 1840
## 3196 1840
## 3197 1820
## 3198 1290
## 3199 1290
## 3200 1290
## 3201 1290
## 3202 1290
## 3424 4290
## 3464 1460
## 3465 1600
## 3466 1840
## 3467 1840
## 3468 1460
## 3469 1600
## 3470 1840
## 3471 1600
## 3472 1740
## 3473 1710
## 3474 1460
## 3475 1740
## 3476 1830
## 3477 1740
## 3478 1290
## 3479 1290
## 3480 1290
## 3481 1290
## 3482 1290
## 3483 1290
## 3484 1290
## 3485 1840
## 3486 1600
## 3487 1840
## 3488 1710
## 3489 1740
## 3490 1710
## 3491 1840
## 3492 1600
## 3493 1840
## 3494 1460
## 3495 1290
## 3496 1290
## 3497 1290
## 3523 3980
## 3837 4480
## 3918 6340
## 3919 5980
## 4055 4110
## 4056 900
## 4248 2610
## 4285 4180
## 4391 3140
## 4435 4330
## 4571 3430
## 4648 5790
## 4649 2410
## 4671 7810
## 4695 1430
## 4696 5330
## 4740 2900
## 4750 7640
## 4821 890
## 4834 900
## 4840 4740
## 4934 4210
## 5083 5830
## 5491 2960
## 5494 3010
## 5495 2960
## 5496 2960
## 5497 2950
## 5549 4130
## 5935 5640
## 6055 3500
## 6230 3320
## 6231 3530
## 6232 3720
## 6233 3150
## 6234 3340
## 6235 3320
## 6236 3340
## 6237 3320
## 6238 3060
## 6239 3530
## 6429 3290
## 6430 2450
## 6431 2750
## 6432 3010
## 6433 3200
## 6434 3200
## 6435 3620
## 6436 2810
## 6437 2550
## 6438 2440
## 6439 3160
## 6440 3400
## 6441 2960
## 6442 3110
## 6443 2900
## 6444 3220
## 6445 2510
## 6446 2970
## 6447 3470
## 6448 2580
## 6449 3590
## 6450 3890
## 6451 2520
## 6452 2990
## 6453 3620
## 6454 3300
## 6455 2830
## 6456 2680
## 6457 3330
## 6512 5040
## 6527 5050
## 6739 3850
## 6766 2550
## 6796 4000
## 6821 4200
## 6931 4000
## 6938 3970
## 6939 4610
## 6940 3360
## 6941 3370
## 6942 4390
## 6943 4380
## 6944 4790
## 6945 3970
## 6946 3370
## 6947 3260
## 6948 3210
## 7039 5320
## 7147 5370
## 7167 4460
## 7210 4460
## 7211 3640
## 7446 2650
## 7447 2520
## 7448 2655
## 7449 2520
## 7450 2515
## 7451 2510
## 7452 2520
## 7453 2630
## 7454 2640
## 7455 2530
## 7456 2520
## 7457 2640
## 7458 2510
## 7459 2445
## 7460 2515
## 7461 2475
## 7462 2460
## 7463 2475
## 7507 5150
## 7649 4350
## 7650 4350
## 7791 5620
## 7871 6650
## 8119 4200
## 8154 3960
## 8232 5150
## 8262 13540
## 8320 5820
## 8377 8750
## 8457 3090
## 8458 550
## 8535 4420
## 8541 3130
## 8698 3380
## 8710 4950
## 8763 3460
## 8887 6360
## 8911 6280
## 8946 6280
## 9215 1650
## 9293 5830
## 9369 3240
## 9420 4800
## 9453 4610
## 9528 7110
## 9546 4480
## 9722 2900
## 10125 6680
## 10318 5150
## 10371 4930
## 10418 4770
## 10623 4570
## 10707 2630
## 10723 4790
## 10741 4200
## 10787 4640
## 10844 1800
## 10958 4010
## 10995 9070
## 11165 4140
## 11289 3310
## 11413 2610
## 11558 730
## 11586 2770
## 11728 2280
## 11758 4930
## 11772 6600
## 11822 4240
## 11898 3690
## 11899 1230
## 11982 7640
## 11992 1670
## 12212 820
## 12255 1650
## 12256 3260
## 12392 2140
## 12472 3150
## 12487 5000
## 12577 5030
## 12582 7070
## 12643 4690
## 12686 3720
## 12759 4380
## 12764 6990calculate leverage, cook’s distance and covariance ratios
homesales$cooks.distance <- cooks.distance(homesales2)
homesales$leverage <- hatvalues(homesales2)
homesales$covariance.ratios <- covratio(homesales2)
homesales[homesales$large.residual, c("cooks.distance", "leverage", "covariance.ratios")]## cooks.distance leverage covariance.ratios
## 6 0.0003786119 3.206527e-04 0.9991633
## 25 0.0008996870 6.219188e-04 0.9991345
## 115 0.0040741281 1.735686e-03 0.9991324
## 160 0.0014918590 1.334527e-03 1.0002574
## 178 0.0013674027 9.234733e-04 0.9993943
## 239 0.0001783162 1.573739e-04 0.9990592
## 246 0.0051550064 1.596054e-03 0.9978968
## 287 0.0008192822 4.950746e-04 0.9987487
## 295 0.0010288656 6.526365e-04 0.9990039
## 300 0.0089655448 2.676565e-03 0.9988337
## 341 0.0004153141 3.885293e-04 0.9993703
## 344 0.0103999269 8.403722e-03 1.0072495
## 359 0.0025140509 1.266065e-03 0.9991103
## 385 0.0034436518 1.273529e-03 0.9982258
## 396 0.0019727976 9.956501e-04 0.9988445
## 475 0.0007174399 5.259101e-04 0.9991408
## 482 0.0016488903 1.368855e-03 1.0001840
## 508 0.0037460466 2.244823e-03 1.0004866
## 528 0.0013766838 1.016638e-03 0.9996449
## 576 0.0012653507 1.221090e-03 1.0002451
## 661 0.0043654857 2.721463e-03 1.0010461
## 670 0.0026620678 5.532028e-04 0.9948897
## 679 0.0110155133 2.968427e-03 0.9986792
## 784 0.0022094263 1.413021e-03 0.9997821
## 802 0.0012580374 1.206275e-03 1.0002220
## 811 0.0050272267 7.379854e-04 0.9925994
## 853 0.0007886185 7.034817e-04 0.9996209
## 877 0.0021996661 1.229049e-03 0.9993166
## 916 0.0056933033 2.243517e-03 0.9994060
## 1009 0.0003070119 2.615081e-04 0.9991125
## 1119 0.0027951267 1.263876e-03 0.9988276
## 1142 0.0020380856 1.029285e-03 0.9988799
## 1155 0.0195775221 6.981544e-03 1.0038587
## 1305 0.0018071616 1.433052e-03 1.0001782
## 1368 0.0011232454 1.094906e-03 1.0001315
## 1380 0.0002658155 2.074826e-04 0.9989253
## 1442 0.0010899082 6.843401e-04 0.9990156
## 1492 0.0006205572 5.128773e-04 0.9993195
## 1504 0.0084924616 3.019928e-03 0.9998461
## 1550 0.0012901280 7.732854e-04 0.9990106
## 1633 0.0002581482 2.006823e-04 0.9989120
## 1650 0.0180781135 4.075723e-03 0.9988962
## 1716 0.0012360741 5.309096e-04 0.9979482
## 1745 0.0015802035 7.162464e-04 0.9982853
## 1870 0.0090535902 5.660062e-03 1.0040160
## 1962 0.0034523123 1.057159e-03 0.9973119
## 1963 0.0003313060 2.121601e-04 0.9985814
## 1964 0.0013690239 4.055014e-04 0.9965220
## 1976 0.0014186714 2.483554e-04 0.9934698
## 1977 0.0010989366 1.748296e-04 0.9926865
## 1978 0.0011303787 1.845172e-04 0.9928937
## 1979 0.0010854651 1.734164e-04 0.9927179
## 1980 0.0010861113 1.727814e-04 0.9926841
## 1981 0.0016516685 3.025577e-04 0.9938376
## 1982 0.0013259343 2.257156e-04 0.9932465
## 2022 0.0022503071 8.641750e-04 0.9979396
## 2099 0.0008212073 5.675052e-04 0.9990795
## 2137 0.0006314130 2.470687e-04 0.9973817
## 2157 0.0008458614 4.289362e-04 0.9982885
## 2257 0.0002424133 2.077547e-04 0.9990677
## 2264 0.0029822023 8.795848e-04 0.9969791
## 2302 0.0020485512 1.322888e-03 0.9997104
## 2360 0.0006568707 3.769444e-04 0.9985214
## 2361 0.0022719723 5.624629e-04 0.9958567
## 2469 0.0003484108 1.726631e-04 0.9979750
## 2604 0.0001736068 1.548624e-04 0.9990717
## 2684 0.0010750288 1.799420e-04 0.9930770
## 2685 0.0012827808 2.268448e-04 0.9935193
## 2686 0.0020716549 4.314632e-04 0.9947810
## 2687 0.0011775318 2.010374e-04 0.9932430
## 2688 0.0010261141 1.685239e-04 0.9929239
## 2689 0.0018898151 3.805644e-04 0.9945264
## 2690 0.0019433263 3.969598e-04 0.9946299
## 2699 0.0610004015 2.504189e-02 1.0229761
## 2708 0.0016526131 5.956223e-04 0.9974588
## 2709 0.0019542860 8.011953e-04 0.9980811
## 2710 0.0020945930 8.143143e-04 0.9979291
## 2717 0.0044039902 1.190442e-03 0.9969074
## 2742 0.0006129755 3.396996e-04 0.9984073
## 2852 0.0448084144 7.459410e-03 1.0003742
## 2867 0.0008756189 8.643949e-04 0.9999165
## 2934 0.0012349398 5.309096e-04 0.9979509
## 2937 0.0011933361 5.309096e-04 0.9980482
## 3097 0.0037436999 1.062350e-03 0.9969966
## 3102 0.0010527025 5.305816e-04 0.9983753
## 3110 0.0006043130 3.882771e-04 0.9987642
## 3111 0.0004289112 3.539678e-04 0.9991582
## 3168 0.0048353662 3.422295e-04 0.9831861
## 3169 0.0048353662 3.422295e-04 0.9831861
## 3170 0.0037900061 2.797401e-04 0.9838369
## 3171 0.0031633555 2.370321e-04 0.9840432
## 3172 0.0032591200 2.433284e-04 0.9839902
## 3173 0.0031680599 2.374391e-04 0.9840474
## 3174 0.0032584052 2.432677e-04 0.9839897
## 3175 0.0041317843 2.988310e-04 0.9835142
## 3176 0.0030827320 2.339303e-04 0.9842462
## 3177 0.0028845637 2.189748e-04 0.9842373
## 3178 0.0028861594 2.191171e-04 0.9842390
## 3179 0.0036231322 2.667836e-04 0.9837840
## 3180 0.0028884200 2.193161e-04 0.9842412
## 3181 0.0036216846 2.666649e-04 0.9837832
## 3182 0.0048370220 3.423599e-04 0.9831869
## 3183 0.0048340335 3.421243e-04 0.9831854
## 3184 0.0048340335 3.421243e-04 0.9831854
## 3185 0.0048372178 3.423753e-04 0.9831870
## 3186 0.0048353662 3.422295e-04 0.9831861
## 3187 0.0048353662 3.422295e-04 0.9831861
## 3188 0.0048480604 3.432253e-04 0.9831920
## 3189 0.0041297057 2.986639e-04 0.9835131
## 3190 0.0032550812 2.429833e-04 0.9839869
## 3191 0.0041288784 2.985973e-04 0.9835127
## 3192 0.0031637968 2.370706e-04 0.9840436
## 3193 0.0032543520 2.429204e-04 0.9839863
## 3194 0.0032538755 2.428792e-04 0.9839859
## 3195 0.0028853418 2.190444e-04 0.9842382
## 3196 0.0028870095 2.191922e-04 0.9842399
## 3197 0.0030945613 2.349509e-04 0.9842557
## 3198 0.0048404537 3.426297e-04 0.9831885
## 3199 0.0048401663 3.426072e-04 0.9831884
## 3200 0.0048340335 3.421243e-04 0.9831854
## 3201 0.0048340335 3.421243e-04 0.9831854
## 3202 0.0048340335 3.421243e-04 0.9831854
## 3424 0.0006578619 3.551590e-04 0.9983634
## 3464 0.0040509577 2.985521e-04 0.9838307
## 3465 0.0037005325 2.782561e-04 0.9841418
## 3466 0.0028284732 2.189086e-04 0.9845474
## 3467 0.0028320388 2.192327e-04 0.9845512
## 3468 0.0040531208 2.987298e-04 0.9838319
## 3469 0.0035460814 2.660647e-04 0.9840941
## 3470 0.0028276297 2.188305e-04 0.9845464
## 3471 0.0037021298 2.783914e-04 0.9841428
## 3472 0.0031033652 2.370624e-04 0.9843564
## 3473 0.0031949437 2.431432e-04 0.9843019
## 3474 0.0040582632 2.991506e-04 0.9838347
## 3475 0.0031080513 2.374757e-04 0.9843605
## 3476 0.0028553700 2.207114e-04 0.9845291
## 3477 0.0031064222 2.373330e-04 0.9843592
## 3478 0.0047444125 3.421243e-04 0.9835072
## 3479 0.0047444125 3.421243e-04 0.9835072
## 3480 0.0047444125 3.421243e-04 0.9835072
## 3481 0.0047444125 3.421243e-04 0.9835072
## 3482 0.0047444125 3.421243e-04 0.9835072
## 3483 0.0047444214 3.421251e-04 0.9835072
## 3484 0.0047443858 3.421222e-04 0.9835072
## 3485 0.0031159380 2.422344e-04 0.9846414
## 3486 0.0035453360 2.660015e-04 0.9840936
## 3487 0.0029685404 2.302604e-04 0.9845940
## 3488 0.0031919770 2.428828e-04 0.9842993
## 3489 0.0031015990 2.369040e-04 0.9843546
## 3490 0.0031950517 2.431526e-04 0.9843020
## 3491 0.0028273493 2.188044e-04 0.9845460
## 3492 0.0037007925 2.782782e-04 0.9841420
## 3493 0.0028291972 2.189752e-04 0.9845482
## 3494 0.0040536602 2.987741e-04 0.9838322
## 3495 0.0047444214 3.421251e-04 0.9835072
## 3496 0.0047444214 3.421251e-04 0.9835072
## 3497 0.0047444214 3.421251e-04 0.9835072
## 3523 0.0026508257 9.226346e-04 0.9976642
## 3837 0.0008982730 5.199545e-04 0.9986833
## 3918 0.0017526328 1.263876e-03 0.9998524
## 3919 0.0013206358 1.029285e-03 0.9997460
## 4055 0.0007882483 3.407559e-04 0.9977764
## 4056 0.0058836897 9.494907e-04 0.9935725
## 4248 0.0011810632 1.170288e-03 1.0002278
## 4285 0.0004103083 3.240811e-04 0.9990607
## 4391 0.0020970477 1.802946e-03 1.0006712
## 4435 0.0004925569 3.746697e-04 0.9990510
## 4571 0.0007270647 7.104353e-04 0.9997493
## 4648 0.1800856691 1.003828e-02 0.9883132
## 4649 1.1769957921 4.365379e-02 1.0128200
## 4671 0.0046273853 3.142908e-03 1.0016339
## 4695 0.0016467356 2.602263e-04 0.9927196
## 4696 0.0019306262 7.541541e-04 0.9978840
## 4740 0.0002836988 2.351624e-04 0.9990459
## 4750 0.0022546554 2.243517e-03 1.0013103
## 4821 0.0007627341 3.662813e-04 0.9980887
## 4834 0.0019306063 8.641750e-04 0.9983990
## 4840 0.0204438832 6.981544e-03 1.0037047
## 4934 0.0016263328 9.335410e-04 0.9990796
## 5083 0.1320504653 2.973075e-02 1.0254461
## 5491 0.0001929156 1.654051e-04 0.9990259
## 5494 0.0001911179 1.673503e-04 0.9990581
## 5495 0.0001938638 1.660483e-04 0.9990251
## 5496 0.0001930188 1.654742e-04 0.9990258
## 5497 0.0001948333 1.660888e-04 0.9990182
## 5549 0.0005138256 4.461296e-04 0.9993250
## 5935 0.0022001806 9.567101e-04 0.9984101
## 6055 0.0016298308 1.273361e-03 0.9999946
## 6230 0.0016145639 1.970646e-04 0.9903512
## 6231 0.0018602312 2.363573e-04 0.9907890
## 6232 0.0019495726 2.550420e-04 0.9910873
## 6233 0.0016180218 1.926846e-04 0.9900947
## 6234 0.0016248097 1.989621e-04 0.9903860
## 6235 0.0016134663 1.969388e-04 0.9903515
## 6236 0.0016241298 1.988838e-04 0.9903862
## 6237 0.0016764588 2.052034e-04 0.9903882
## 6238 0.0016046873 1.883606e-04 0.9899398
## 6239 0.0018608539 2.364312e-04 0.9907889
## 6429 0.0047518776 1.929573e-04 0.9702076
## 6430 0.0044575261 1.669673e-04 0.9676663
## 6431 0.0045203752 1.745775e-04 0.9686498
## 6432 0.0044307491 1.753499e-04 0.9694102
## 6433 0.0042880911 1.720489e-04 0.9698255
## 6434 0.0046572420 1.874667e-04 0.9699389
## 6435 0.0054560138 2.286800e-04 0.9711775
## 6436 0.0044421539 1.727114e-04 0.9688582
## 6437 0.0042731544 1.615057e-04 0.9679506
## 6438 0.0047499885 1.780232e-04 0.9676957
## 6439 0.0043885199 1.757414e-04 0.9697711
## 6440 0.0049617830 2.035737e-04 0.9705262
## 6441 0.0044736804 1.761038e-04 0.9692461
## 6442 0.0045447637 1.814312e-04 0.9696819
## 6443 0.0038911815 1.748394e-04 0.9730759
## 6444 0.0040840289 1.894174e-04 0.9739375
## 6445 0.0045098703 1.953908e-04 0.9720906
## 6446 0.0041026237 1.859288e-04 0.9733188
## 6447 0.0044755781 2.129193e-04 0.9746209
## 6448 0.0039017399 1.696550e-04 0.9721662
## 6449 0.0047319781 2.279179e-04 0.9749511
## 6450 0.0056553251 2.808689e-04 0.9757691
## 6451 0.0042406567 1.835807e-04 0.9720564
## 6452 0.0041075973 1.865188e-04 0.9733719
## 6453 0.0049496689 2.395539e-04 0.9750845
## 6454 0.0041813564 1.955152e-04 0.9741566
## 6455 0.0038882018 1.735664e-04 0.9728966
## 6456 0.0039983513 1.758944e-04 0.9724971
## 6457 0.0042297917 1.983749e-04 0.9742377
## 6512 0.0029029073 7.199107e-04 0.9960231
## 6527 0.0008947873 6.217587e-04 0.9991437
## 6739 0.0004613583 2.914610e-04 0.9986343
## 6766 0.0076877384 7.564572e-03 1.0066716
## 6796 0.0003264600 3.083179e-04 0.9993026
## 6821 0.0013239946 1.040755e-03 0.9997710
## 6931 0.0003315936 2.768138e-04 0.9990982
## 6938 0.0010770205 3.022898e-04 0.9961871
## 6939 0.0014447326 4.778399e-04 0.9970320
## 6940 0.0008567372 2.080121e-04 0.9954035
## 6941 0.0008520316 2.075052e-04 0.9954186
## 6942 0.0013055232 4.075967e-04 0.9967389
## 6943 0.0013019166 4.053457e-04 0.9967257
## 6944 0.0015577149 5.409615e-04 0.9972739
## 6945 0.0010770205 3.022898e-04 0.9961871
## 6946 0.0008579593 2.088057e-04 0.9954164
## 6947 0.0008386385 1.990590e-04 0.9952776
## 6948 0.0008297585 1.948163e-04 0.9952161
## 7039 0.0014192040 1.105810e-03 0.9998223
## 7147 0.0013316292 7.756072e-04 0.9989526
## 7167 0.0067486219 6.659268e-04 0.9884256
## 7210 0.0046751759 1.043304e-03 0.9957909
## 7211 0.0029470393 5.522945e-04 0.9942399
## 7446 0.0027496462 1.882051e-04 0.9824416
## 7447 0.0028905678 1.947612e-04 0.9821637
## 7448 0.0027435033 1.879167e-04 0.9824539
## 7449 0.0028916806 1.948163e-04 0.9821619
## 7450 0.0028981562 1.951341e-04 0.9821511
## 7451 0.0029046674 1.954546e-04 0.9821404
## 7452 0.0028900522 1.947369e-04 0.9821646
## 7453 0.0026134937 1.780907e-04 0.9823514
## 7454 0.0026044760 1.776953e-04 0.9823732
## 7455 0.0027166350 1.828912e-04 0.9821368
## 7456 0.0028906475 1.947650e-04 0.9821635
## 7457 0.0027593031 1.886302e-04 0.9824196
## 7458 0.0029029724 1.953748e-04 0.9821436
## 7459 0.0029966823 2.000699e-04 0.9820014
## 7460 0.0028981562 1.951341e-04 0.9821511
## 7461 0.0029525764 1.978397e-04 0.9820655
## 7462 0.0029742694 1.989330e-04 0.9820334
## 7463 0.0029525458 1.978383e-04 0.9820656
## 7507 0.0027068028 1.413021e-03 0.9993448
## 7649 0.0004269719 3.991099e-04 0.9993798
## 7650 0.0004273070 3.994994e-04 0.9993804
## 7791 0.0017592217 1.514207e-03 1.0003830
## 7871 0.0077407189 2.979407e-03 1.0000710
## 8119 0.0010738887 1.040755e-03 1.0000698
## 8154 0.0003579616 3.038300e-04 0.9991497
## 8232 0.0027270564 1.413021e-03 0.9993270
## 8262 0.0358408052 1.073599e-02 1.0070189
## 8320 0.0110337357 4.680867e-03 1.0020852
## 8377 0.6636528396 6.370680e-02 1.0554687
## 8457 0.0003209938 2.121601e-04 0.9986418
## 8458 0.0013399647 4.055014e-04 0.9966109
## 8535 0.0005038155 4.160318e-04 0.9992212
## 8541 0.0002597440 2.006823e-04 0.9989021
## 8698 0.0002953519 2.133484e-04 0.9988029
## 8710 0.0034828842 6.275339e-04 0.9940502
## 8763 0.0006188175 3.892478e-04 0.9987237
## 8887 0.0104601632 1.330079e-03 0.9918923
## 8911 0.0016479316 1.216828e-03 0.9998455
## 8946 0.0016479316 1.216828e-03 0.9998455
## 9215 0.0042542061 2.576135e-03 1.0008412
## 9293 0.0014100380 1.016638e-03 0.9996042
## 9369 0.0023524641 2.036880e-03 1.0009163
## 9420 0.0085285048 5.204139e-03 1.0035062
## 9453 0.0006515232 5.309096e-04 0.9993161
## 9528 0.0095261587 2.136525e-03 0.9969157
## 9546 0.0008603946 5.199545e-04 0.9987738
## 9722 0.0004952458 2.351624e-04 0.9979281
## 10125 0.0020786427 1.678259e-03 1.0004522
## 10318 0.0261844364 2.222189e-02 1.0215795
## 10371 0.0009624012 6.752997e-04 0.9992147
## 10418 0.0020804200 1.630009e-03 1.0003569
## 10623 0.0006826384 5.861345e-04 0.9994492
## 10707 0.0001214075 9.981802e-05 0.9988982
## 10723 0.0006302687 5.334653e-04 0.9993755
## 10741 0.0003508417 3.469648e-04 0.9994005
## 10787 0.0045484606 1.349635e-03 0.9974755
## 10844 0.0023988819 1.597504e-03 1.0000442
## 10958 0.0006636672 3.940425e-04 0.9986111
## 10995 0.0044475345 3.705608e-03 1.0025388
## 11165 0.0005876438 3.254236e-04 0.9983914
## 11289 0.0010351137 2.207959e-04 0.9947106
## 11413 0.0046745001 1.158445e-03 0.9964591
## 11558 0.0044728700 6.238003e-04 0.9920420
## 11586 0.0028588670 1.076254e-03 0.9980872
## 11728 0.0119150426 4.675383e-03 1.0018422
## 11758 0.0010313489 6.752997e-04 0.9990878
## 11772 0.0167299080 1.496278e-03 0.9879681
## 11822 0.0022709876 3.299199e-04 0.9921025
## 11898 0.0663281580 3.418654e-02 1.0333064
## 11899 0.1463847873 3.690804e-02 1.0337185
## 11982 0.0111575241 2.243517e-03 0.9963857
## 11992 0.1259398797 4.502498e-03 0.9704760
## 12212 0.0027848613 1.538777e-03 0.9996024
## 12255 0.0037819076 1.348070e-03 0.9981747
## 12256 0.0018448651 1.092883e-03 0.9993064
## 12392 0.0011421621 8.560378e-04 0.9995087
## 12472 0.0035237958 6.248723e-04 0.9939372
## 12487 0.0037885394 1.288023e-03 0.9979458
## 12577 0.0062196039 1.352017e-03 0.9959528
## 12582 0.0322490030 2.443888e-03 0.9864407
## 12643 0.0071298373 4.740877e-04 0.9822009
## 12686 0.0002249663 2.063750e-04 0.9991617
## 12759 0.0004195772 3.964855e-04 0.9993916
## 12764 0.0095134947 2.178446e-03 0.9970713k. none of the values in cook’s distance is greater than 1, so none of the cases is having an undue influence on the model. the average leverage is equal to 4/12865=3.10e-04 and all cases are within boundary of the 3 times the average and many cases are close to 2 times the average.
covariance ration should be between [1 + 3(4/12865)] = 1.0009 and [1-3(4/12865)] = 0.999
there are many cases outside but very close to these boundaries. However given the Cook’s distance no or little cause for alarm
##dwtest(homesales2)l.the DW value is 0.56049, which means the value is within the limits. anything greater than 3 or less than 1 should raise alarm.
Perform the necessary calculations to assess the assumption of no multicollinearity and state if the condition is met or not.
##vif(homesales2)
##1/vif(homesales2)
##mean(vif(homesales2))m. The laregest vif(1.16) is not greater than 10. The tolerance values are well above 0.2 and the average VIF is 1.1605. All these values indicate there is no collinearity within the data.
use plot() and hist() functions
plot(homesales2)
hist(homesales$studentized.residuals)
#### n. I think the fitted values against residuals indicates the values are evenly distributed around 0. So I assume that this is linear graph. I don’t see any funnel type data. So it is does not violate homoscedasticity #### o. The histogram for residulas looks similar to bell shape. So the data is not skewed and it is not biased either. Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.