Advertisements
Advertisements
Question
Find the regression equation Y on X and X on Y for the following data:
| Y | 45 | 48 | 50 | 55 | 65 | 70 | 75 | 72 | 80 | 85 |
| X | 25 | 30 | 35 | 30 | 40 | 50 | 45 | 55 | 60 | 65 |
Solution
| X | Y | dx=X -45 | dy=Y -65 | dx2 | dy2 | dxdy |
| 25 | 45 | -20 | -20 |
(20×20)400 |
(20×20)400 | (20×20)400 |
| 30 | 48 | -15 | -17 | (15×15)225 | (18×17)289 | (15×17)255 |
| 35 | 50 | -10 | -15 | (10×10)100 | (15×15)225 | (10×15)150 |
| 30 | 55 | -15 | -10 | (15×15)225 | (10×10)100 | (15×10)150 |
| 40 | 65 | -5 | 0 | (5×5)25 | (0×0)0 | (5×0)0 |
| 50 | 70 | 5 | 5 | (5×5)25 | (5×5)25 | (5×5)25 |
| 45 | 75 | 0 | 10 | (0×0)0 | (10×10)100 | (0×10)0 |
| 55 | 72 | 10 | 7 | (10×10)100 | (7×7)49 | (10×7)70 |
| 60 | 80 | 15 | 15 | (15×15)225 | (15×15)225 | (15×15)225 |
| 65 | 85 | 20 | 20 | (20×20)400 | (20×20)400 | (20×20)400 |
| 435[435 ÷10]=43.5 | 645[645 ÷10]=64.5 |
[(-65)-(+50)] =[-15] |
[(-63)-(+57)] =[-6] |
[Total] 1725 |
[Total] 1813 |
[Total] 1675 |
`b_(x_y)=(Nsumd_Xd_Y -(sumd_X)(sumd_Y))/(Nsumd_(Y^2)-(sumd_Y)^2)`
`= ((10)(1675) -(-15)(-5))/(10(1813)-(-5)^2)`
`= (16750-75)/(18130-25)`
`= (16675)/(18105)`
= 0.92
X on Y
`X-barX` = bxy (`Y-barY`)
X- 43.5 = 0.92 (Y- 64.5)
X - 43.5 = 0.92Y - 59.34
X = 0.92Y - 59.34 + 43.5
X = 0.92Y - 15.84
`b_(x_y)=(Nsumd_Xd_Y -(sumd_X)(sumd_Y))/(Nsumd_(Y^2)-(sumd_Y)^2)`
`= ((10)(1675) -(-15)(-5))/(10(1725)-(-15)^2)`
= `16675/17025`
= 0.98
Y on X
`Y-barY` = bxy (`X-barX`)
Y - 64.5 = 0.98 (X - 43.5)
Y - 64.5 = 0.98X - 42.63
Y = 0.98X - 21.87
Regression X on Y
X = 0.92Y - 15.84
Regression Y on X
Y = 0.98X - 21.87
APPEARS IN
RELATED QUESTIONS
Choose the correct alternative:
Regression analysis is the theory of
Choose the correct alternative:
We can estimate the value of one variable with the help of other known variable only if they are
Choose the correct alternative.
‘r’ is __________.
Choose the correct alternative.
bXY .bYX is _________.
|bxy + byx | ≥ _______
bxy and byx are _______.
Choose the correct alternative.
Corr (x, y) = _____
Choose the correct alternative.
Regression equation of Y on X is ____
State whether the following statement is True or False:
The variable used for predicting the response is called the independent variable
Dependent variables are also known as ______
The term regression was used by:
The purpose of simple linear regression analysis is to:
A process by which we estimate the value of dependent variable on the basis of one or more independent variables is called:
In the regression equation Y = β0 +β1 X, the X is called:
Define Regression.
Mention the uses of Regression Analysis.
If Y = 2 - 0.2X, then the value of the Y-intercept is equal to ______.
