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Question
The following are the marks obtained by the students in Economics (X) and Mathematics (Y)
| X | 59 | 60 | 61 | 62 | 63 |
| Y | 78 | 82 | 82 | 79 | 81 |
Find the regression equation of Y on X.
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Solution
X = Marks obtained in Economics
Y = Marks obtained in Mathematics
| X = xi | Y = yi | `"x"_"i"^2` | xi yi |
| 59 | 78 | 3481 | 4602 |
| 60 | 82 | 3600 | 4920 |
| 61 | 82 | 3721 | 5002 |
| 62 | 79 | 3844 | 4898 |
| 63 | 81 | 3969 | 5103 |
| 305 | 402 | 18615 | 24525 |
From the table, we have
n = 5, ∑ xi = 305, ∑ yi = 402, `sum "x"_"i"^2 = 18615`, ∑ xi yi = 24525
`bar"x" = (sum "x"_"i")/"n" = 305/5 = 61`
`bar"y" = (sum "y"_"i")/"n" = 402/5 = 80.4`
Now, `"b"_"YX" = (sum"x"_"i" y_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (24525 - 5 xx 61 xx 80.4)/(18615 - 5(61)^2)`
`= (24525 - 24522)/(18615 - 18605) = 3/10` = 0.3
Also, `"a" = bar"y" - "b"_"YX" bar"x"`
= 80.4 - (0.3)(61) = 80.4 - 18.3 = 62.1
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 62.1 + 0.3 X
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