### Multiple Regression Using R

2019-09-15 Manoj Pawar

Multiple regression is extended version of linear regression.we have more than one predictor and one response variable.

Step to follow:

Step 1:multiple regression follows given equation,

``    Z <- a+b1x1+b1x2+…+bnxn``

Where,

Z :is the Response Variable.

A,b1,b2..bn:are Coefficient.

X1,x2,…xn:are Pridictor Variable.

Step 2:lm() function

lm() function find out the relation between two variable (i.e linear regression)  or more than two variable (i.e multiple regression).

``lm(Y~x1+x2+x3..,data)``

Example: we are using dataset avilable in R environment (i.e:mtcars).how dataset can access is given below:

`````` > data("mtcars")

> print.data.frame(mtcars)
``````

shows mtcars dataset,

``````                      mpg   cyl  disp  hp  drat   wt  qsec  vs am gear carb
Mazda RX4            21.0   6   160.0 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag        21.0   6   160.0 110 3.90 2.875 17.02  0  1    4    4
Datsun 710           22.8   4   108.0  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive       21.4   6   258.0 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout    18.7   8   360.0 175 3.15 3.440 17.02  0  0    3    2
Valiant              18.1   6   225.0 105 2.76 3.460 20.22  1  0    3    1
Duster 360           14.3   8   360.0 245 3.21 3.570 15.84  0  0    3    4
Merc 240D            24.4   4   146.7  62 3.69 3.190 20.00  1  0    4    2
``````

when we want to display only 6 columns in the dataset, then

`````` w <- head(mtcars,6)

print(w)``````

it will display 6 columns from mtcars,

``````                      mpg   cyl  disp  hp  drat   wt
Mazda RX4            21.0   6   160.0 110 3.90 2.620
Mazda RX4 Wag        21.0   6   160.0 110 3.90 2.875
Datsun 710           22.8   4   108.0  93 3.85 2.320
Hornet 4 Drive       21.4   6   258.0 110 3.08 3.215
Hornet Sportabout    18.7   8   360.0 175 3.15 3.440
Valiant              18.1   6   225.0 105 2.76 3.460
Duster 360           14.3   8   360.0 245 3.21 3.570
Merc 240D            24.4   4   146.7  62 3.69 3.190
``````

Using vectors also we can derive dataset in r environment,

``````    input<-mtcars[,c("mpg","disp","hp","wt","cyl")]

print(input)``````

following result show dataset of mtcars that contain those content which are passing to vectcor:

``````                      mpg     disp   hp     wt   cyl
Mazda RX4            21.0    160.0  110  2.620   6
Mazda RX4 Wag        21.0    160.0  110  2.875   6
Datsun 710           22.8    108.0   93  2.320   4
Hornet 4 Drive       21.4    258.0  110  3.215   6
Hornet Sportabout    18.7    360.0  175  3.440   8
Valiant              18.1    225.0  105  3.460   6
Duster 360           14.3    360.0  245  3.570   8
Merc 240D            24.4    146.7   62  3.190   4
``````

Then we find relation among those variable using lm() function

``````   model<-lm(mpg~disp+hp+wt+cyl,data = input)

print(model)``````

than it will show following result,

``````  Call:

lm(formula = mpg ~ disp + hp + wt + cyl, data = input)

Coefficients:

(Intercept)         disp           hp           wt          cyl

40.82854      0.01160     -0.02054     -3.85390     -1.29332``````

Finally we find milege from disp,hp,wt and cyl using following formula,

``   Y = a+disp*x1+hp*x2+wt*x3+cyl*x4``

or

``````   z=40.82854+(0.01160)*160+(-0.02054)*110+(-3.85390)*2.620+(-1.29332)*6

print(z)``````

output:

22.568

##### Manoj Pawar

I am data analyst and show you how visualization done using R language.!

-Data Analyst