Linear Regression Using R Studio
> mydata=read.csv(file.choose(), header = T)
> View(mydata)
> attach(mydata)
> #check the dimension of the data set
> dim(mydata)
[1] 545 13
> #to check the variable names
> names(mydata)
[1] "price" "area" "bedrooms" "bathrooms" "stories"
[6] "mainroad" "guestroom" "basement" "hotwaterheating" "airconditioning"
[11] "parking" "prefarea" "furnishingstatus"
> plot(price~area)
> abline(lm(price~area))
> #Simple Linear Regression
> #DV= Price; IDV= Area
> sreg= lm(price~area)
> summary(sreg)
Call:
lm(formula = price ~ area)
Residuals:
Min 1Q Median 3Q Max
-4867112 -1022228 -200135 683027 7484838
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.387e+06 1.745e+05 13.68 <2e-16 ***
area 4.620e+02 3.123e+01 14.79 <2e-16 ***
— -
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1581000 on 543 degrees of freedom
Multiple R-squared: 0.2873, Adjusted R-squared: 0.286
F-statistic: 218.9 on 1 and 543 DF, p-value: < 2.2e-16
> plot(area,price, main = “scatter plot”)
> abline(sreg)
> plot(sreg)
> par(mfrow=c(2,2))
> plot(sreg)
> #Multiple Linaer Regression
> mreg = lm(price~area+bedrooms+bathrooms+stories+mainroad+guestroom+basement+hotwaterheating+airconditioning)
> summary(mreg)
Call:
lm(formula = price ~ area + bedrooms + bathrooms + stories + mainroad + guestroom + basement + hotwaterheating + airconditioning)
Residuals:
Min 1Q Median 3Q Max
-2790328 -642601 -20387 582368 5931692
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -573514.10 247246.32 -2.320 0.020738 *
area 303.30 24.47 12.392 < 2e-16 ***
bedrooms 164594.14 76756.38 2.144 0.032453 *
bathrooms 1041793.18 109119.50 9.547 < 2e-16 ***
stories 445078.09 67889.83 6.556 1.30e-10 ***
mainroad 663026.18 147891.26 4.483 9.00e-06 ***
guestroom 318748.08 139464.36 2.286 0.022673 *
basement 507993.18 114628.11 4.432 1.13e-05 ***
hotwaterheating 919690.70 235479.04 3.906 0.000106 ***
airconditioning 951148.06 113990.62 8.344 6.14e-16 ***
— -
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1134000 on 535 degrees of freedom
Multiple R-squared: 0.6385, Adjusted R-squared: 0.6324
F-statistic: 105 on 9 and 535 DF, p-value: < 2.2e-16
> par(mfrow=c(2,2))
> plot(mreg)
> #Durbin Watson test for Autocorrelation
> install.packages(“lmtest”)
WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:
https://cran.rstudio.com/bin/windows/Rtools/
Installing package into ‘C:/Users/Subho/Documents/R/win-library/4.0’
(as ‘lib’ is unspecified)
also installing the dependency ‘zoo’
trying URL ‘http://cran.rstudio.com/bin/windows/contrib/4.0/zoo_1.8-8.zip'
Content type ‘application/zip’ length 1094462 bytes (1.0 MB)
downloaded 1.0 MB
trying URL ‘http://cran.rstudio.com/bin/windows/contrib/4.0/lmtest_0.9-38.zip'
Content type ‘application/zip’ length 411871 bytes (402 KB)
downloaded 402 KB
package ‘zoo’ successfully unpacked and MD5 sums checked
package ‘lmtest’ successfully unpacked and MD5 sums checked
The downloaded binary packages are in
C:\Users\Subho\AppData\Local\Temp\Rtmp4iikJ9\downloaded_packages
> library(lmtest)
Loading required package: zoo
Attaching package: ‘zoo’
The following objects are masked from ‘package:base’:
as.Date, as.Date.numeric
Warning messages:
1: package ‘lmtest’ was built under R version 4.0.3
2: package ‘zoo’ was built under R version 4.0.3
> dwtest(mreg)
Durbin-Watson test
data: mreg
DW = 1.1538, p-value < 2.2e-16
alternative hypothesis: true autocorrelation is greater than 0
> #VIF to check multicolinearity
> install.packages(“car”)
WARNING: Rtools is required to build R packages but is not currently installed. Please download and install the appropriate version of Rtools before proceeding:
https://cran.rstudio.com/bin/windows/Rtools/
Installing package into ‘C:/Users/Subho/Documents/R/win-library/4.0’
(as ‘lib’ is unspecified)
trying URL ‘http://cran.rstudio.com/bin/windows/contrib/4.0/car_3.0-10.zip'
Content type ‘application/zip’ length 1561500 bytes (1.5 MB)
downloaded 1.5 MB
package ‘car’ successfully unpacked and MD5 sums checked
The downloaded binary packages are in
C:\Users\Subho\AppData\Local\Temp\Rtmp4iikJ9\downloaded_packages
> library(car)
Loading required package: carData
Warning message:
package ‘car’ was built under R version 4.0.3
> car::vif(mreg)
area bedrooms bathrooms stories mainroad guestroom
1.193222 1.357446 1.271540 1.467056 1.124429 1.205831
basement hotwaterheating airconditioning
1.267445 1.028391 1.189285
> hist(price)
> hist(price, freq = F)
> lines(density(price))
