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Question
Compute the appropriate regression equation for the following data:
| X [Independent Variable] |
2 | 4 | 5 | 6 | 8 | 11 |
| Y [dependent Variable] | 18 | 12 | 10 | 8 | 7 | 5 |
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Solution
Since X is independent and Y is dependent variable, we find the regression equation of Y on X.
| X = xi | Y = yi | `"x"_"i"^2` | xi yi |
| 2 | 18 | 4 | 36 |
| 4 | 12 | 16 | 48 |
| 5 | 10 | 25 | 50 |
| 6 | 8 | 36 | 48 |
| 8 | 7 | 64 | 56 |
| 11 | 5 | 121 | 55 |
| 36 | 60 | 266 | 293 |
From the table, we have,
n = 6, ∑ xi = 36, ∑ yi = 60, `sum "x"_"i"^2 = 266`, ∑ xi yi = 293
`bar"x" = (sum "x"_"i")/"n" 36/6 = 6`
`bar"y" = (sum "y"_"i")/"n" = 60/6 = 10`
Now, `"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (293 - 6xx6xx10)/(266 - 6(6)^2) = (293 - 360)/(266 - 216) = (-67)/50`
∴ bYX = - 1.34
Also, `"a"' = bar"y" - "b"_"YX" bar"x"`
= 10 - (- 1.34)(6) = 10 + 8.04 = 18.04
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 18.04 - 1.34 X
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