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