COMMERCIAL ARITHMETIC GRADE 12 ISC MATHEMATICS

1. REGRESSION
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2. THE STATISTICAL METHODS WHICH HELP US IN
PREDICTING THE VALUE OF ONE VARIABLE
GIVEN THE VALUE OF THE OTHER VARIABLE IS
CALLED REGRESSION.
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3. The following results were obtained with respect to 2 variables
x and y
      6,318,184,199,42,30 22
nyxxyyx
Find a) The 2 regression coefficients
b)Correlation coefficient between x and y
c) Regression equation of y on x
d) The most likely value of y when x = 10
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Question 1

4.  
  


 22
)( xxn
yxxyn
byxa)
2
42)318(6
)42)(30()199(6


= -0.46
 
  


 22
)( yyn
yxxyn
bxy
Regression coefficient of
y on x
Regression coefficient of
x on y
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5. 2
)42()318(6
)42)(30()199(6



= -0.46
b) 38.0)46.0)(32.0(  xyyxbbr
c) 7,5 

yx
Correlation coefficient
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r takes the same value as
The regression coefficients

6. Regression equation of y on x is
y-7= -0.32(x-5)
y =-0.32x + 8.6
d) When x = 10, y = 5.4
)(
_
xxbyy yx 

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7. 2 regression lines are represented by 2x + 3y – 10 = 0 and
4x + y – 5 = 0, Find the line of regression of y on x.
3y = -2x + 10
3
10
3
2

x
y
3
2
yxb = slope of the regression line of
y on x
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Question 2
let
be the regression line of y on x

8. 4x + y – 5 = 0
4x = - y + 5
4
5
4

y
x
4
1
xyb Slope of the regression
equation of x on y
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Is the regression line of x on y
if

9. 1
6
1
yxxybb
Regression equation of y on x is 2x +3y – 10 =0
xyyxbbr 
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Our assumption is correct

10. From the equations of the 2 regression lines 4x + 3 y + 7 = 0 and
3x + 4y + 8 = 0, find
i) The mean of x and y
ii) The regression coefficients
iii) The coefficient of correlation
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Question 3

11. Solving the 2 equations simultaneously,
4
11
,
7
4


yx
4x = -3y -7
4
7
4
3
 yx
4
3
xybRegression coefficient of x on y
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let
be the regression equation of x on y

12. 4y = -3x - 8
2
4
3


 xy
4
3
yxb
16
92
r
Regression cooefficient of y on x
4
3
r
xyyxbbr 
r takes the same sign as the regression coefficients
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Let be the regression equation of y on x

13. Fit a straight line to the following data, treating y as the dependent
variable
x 14 12 13 14 12
y 22 23 22 24 24
23,13 

yx
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Question 4

14. x y u= x-13 v= y- 23 uv
14 22 1 -1 -1 1
12 23 -1 0 0 1
13 22 0 -1 0 0
14 24 1 1 1 1
12 24 -1 1 -1 1
65 115 0 0 -1 4
2
u
0,0 

vu  
  


 22
)( uun
vuuvn
byx
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15. 4
1
yxb
We need to find the line of regression of y on x
)(
_
xxbyy yx 

)13(
4
1
23  xy
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Since y is the dependent variable

16. 4y+x = 105
Required line:
********************************
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