Formula

1. `byx = (n * sum fdxdy - sum fdx * sum fdy ) / (n * sum fdx^2 - (sum fdx)^2) * (h_y)/(h_x)`

2. `bxy = (n * sum fdxdy - sum fdx * sum fdy ) / (n * sum fdy^2 - (sum fdy)^2) * (h_x)/(h_y)`

3. Regression Line y on x `y - bar y = byx (x - bar x)`

4. Regression Line x on y `x - bar x = bxy (y - bar y)`

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Examples
2. Find Regression line equations from the following data

Y Class-X	18	19	20	21
350 - 400	1	4	6	10
300 - 350	2	6	8	5
250 - 300	3	5	4	2
200 - 250	4	4	2	1

Solution:

		M.V.`(y)`	18	19	20	21
C.I.`(x)`	M.V.`(x)`	`dy` `dx`	-1 `-1=18-19` `dy=y-19`	0 `0=19-19` `dy=y-19`	1 `1=20-19` `dy=y-19`	2 `2=21-19` `dy=y-19`	`f_x`	`fdx`	`fdx^2`	`fdxdy`
350 - 400	375 `375=(350+400)/2`	1 `1=(375-325)/50` `dx=(x-325)/50`	[-1] `-1=1*1*-1` `f*dx*dy`1	[0] `0=4*1*0` `f*dx*dy`4	[6] `6=6*1*1` `f*dx*dy`6	[20] `20=10*1*2` `f*dx*dy`10	21 `21=1+4+6+10`	21 `21=21*1` `fdx=f_x*dx`	21 `21=21*1` `fdx^2=fdx*dx`	25 `25=-1+0+6+20`
300 - 350	325 `325=(300+350)/2`	0 `0=(325-325)/50` `dx=(x-325)/50`	[0] `0=2*0*-1` `f*dx*dy`2	[0] `0=6*0*0` `f*dx*dy`6	[0] `0=8*0*1` `f*dx*dy`8	[0] `0=5*0*2` `f*dx*dy`5	21 `21=2+6+8+5`	0 `0=21*0` `fdx=f_x*dx`	0 `0=0*0` `fdx^2=fdx*dx`	0 `0=0+0+0+0`
250 - 300	275 `275=(250+300)/2`	-1 `-1=(275-325)/50` `dx=(x-325)/50`	[3] `3=3*-1*-1` `f*dx*dy`3	[0] `0=5*-1*0` `f*dx*dy`5	[-4] `-4=4*-1*1` `f*dx*dy`4	[-4] `-4=2*-1*2` `f*dx*dy`2	14 `14=3+5+4+2`	-14 `-14=14*-1` `fdx=f_x*dx`	14 `14=-14*-1` `fdx^2=fdx*dx`	-5 `-5=3+0-4-4`
200 - 250	225 `225=(200+250)/2`	-2 `-2=(225-325)/50` `dx=(x-325)/50`	[8] `8=4*-2*-1` `f*dx*dy`4	[0] `0=4*-2*0` `f*dx*dy`4	[-4] `-4=2*-2*1` `f*dx*dy`2	[-4] `-4=1*-2*2` `f*dx*dy`1	11 `11=4+4+2+1`	-22 `-22=11*-2` `fdx=f_x*dx`	44 `44=-22*-2` `fdx^2=fdx*dx`	0 `0=8+0-4-4`
		`f_y`	10 `10=1+2+3+4`	19 `19=4+6+5+4`	20 `20=6+8+4+2`	18 `18=10+5+2+1`	67 `n=sum f_x=67=21+21+14+11` OR `n=sum f_y=67=10+19+20+18`	-15 `sum fdx=-15=21+0-14-22`	79 `sum fdx^2=79=21+0+14+44`	20 `sum fdxdy=20=25+0-5+0`
		`fdy`	-10 `-10=10*-1` `fdy=f_y*dy`	0 `0=19*0` `fdy=f_y*dy`	20 `20=20*1` `fdy=f_y*dy`	36 `36=18*2` `fdy=f_y*dy`	46 `sum fdy=46=-10+0+20+36`
		`fdy^2`	10 `10=-10*-1` `fdy^2=fdy*dy`	0 `0=0*0` `fdy^2=fdy*dy`	20 `20=20*1` `fdy^2=fdy*dy`	72 `72=36*2` `fdy^2=fdy*dy`	102 `sum fdy^2=102=-10+0+20+36`
		`fdxdy`	10 `10=-1+0+3+8`	0 `0=0+0+0+0`	-2 `-2=6+0-4-4`	12 `12=20+0-4-4`	20 `sum fdxdy=20=10+0-2+12`

`bar X = A + (sum fdx)/n * h_x`

`=325 + -15/67 * 50`

`=325 + -0.2239 * 50`

`=325 + -11.194`

`=313.806`


`bar Y = B + (sum fdy)/n * h_y`

`=19 + 46/67 * 1`

`=19 + 0.6866 * 1`

`=19 + 0.6866`

`=19.6866`


`byx = (n * sum fdxdy - sum fdx * sum fdy ) / (n * sum fdx^2 - (sum fdx)^2) * (h_y)/(h_x)`

`=(67 * 20 - -15 * 46 )/(67 * 79 - (-15)^2) * 1/50`

`=(1340 + 690 )/(5293 - 225) * 1/50`

`=2030/5068 * 1/50`

`=0.008`


Regression Line y on x
`y - bar y = byx (x - bar x)`

`y - 19.6866 = 0.008 (x - 313.806)`

`y - 19.6866 = 0.008 x - 2.5139`

`y = 0.008 x - 2.5139 + 19.6866`

`y = 0.008 x + 17.1727`


`bxy = (n * sum fdxdy - sum fdx * sum fdy ) / (n * sum fdy^2 - (sum fdy)^2) * (h_x)/(h_y)`

`=(67 * 20 - -15 * 46 )/(67 * 102 - (46)^2) * 50/1`

`=(1340 + 690 )/(6834 - 2116) * 50/1`

`=2030/4718 * 50/1`

`=21.5134`


Regression Line x on y
`x - bar x = bxy (y - bar y)`

`x - 313.806 = 21.5134 (y - 19.6866)`

`x - 313.806 = 21.5134 y - 423.5241`

`x = 21.5134 y - 423.5241 + 313.806`

`x = 21.5134 y - 109.7181`

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