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प्रश्न
Find the line of best fit for the following data, treating x as the dependent variable (Regression equation x on y):
| X | 14 | 12 | 13 | 14 | 16 | 10 | 13 | 12 |
| Y | 14 | 23 | 17 | 24 | 18 | 25 | 23 | 24 |
Hence, estimate the value of x when y = 16.
उत्तर
| X | Y | `x = "X" - bar"X"` |
`y = "Y" - bar"Y"` | `"x"^2` | `"y"^2` | "xy" |
| 14 | 14 | 14 - 13 = 1 | 14 - 21 = -7 | 1 | 49 | -7 |
| 12 | 23 | 12 - 13 = -1 | 23 - 21 = 2 | 1 | 4 | -2 |
| 13 | 17 | 13 - 13 = 0 | 17 - 21 = -4 | 0 | 16 | 0 |
| 14 | 24 | 14 - 13 = 0 | 24 - 21 = 3 | 1 | 9 | 3 |
| 16 | 18 | 16 - 13 = 3 | 18 - 21 = -3 | 9 | 9 | -9 |
| 10 | 25 | 10 - 13 = -3 | 25 - 21 = 4 | 9 | 16 | -12 |
| 13 | 23 | 13 - 13 = 0 | 23 - 21 = 2 | 0 | 4 | 0 |
| 12 | 24 | 12 -13 = -1 | 24 - 21 = 3 | 1 | 9 | -3 |
| ∑X = 104 | ∑Y = 168 | ∑x2 = 22 | ∑y2 = 116 | ∑xy = -30 |
`bar"X" = 104/8 = 13 , bar"Y" = 168/8 = 21`
`"b"_"xy" = (sum"xy")/(sum"y"^2) = (-30)/116 = -0.259`
Regression equation of x on y is
`"x" - bar"X" = "b"_"xy"("y" - bar"Y")`
`"x" - 13 = (-30)/116("y" - 21)`
58x - 754 = -15y + 315
58x + 15y = 1069
Put y = 16,
58x + 15(16) = 1069
58x + 240 = 1069
58x = 829
x = 14.29
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