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The following information is given. Details X (in ₹) Y (in ₹) Arithmetic Mean 6 8 Standard Deviation 5 403 Coefficient of correlation between X and Y is 815.

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प्रश्न

The following information is given.

Details X (in ₹) Y (in ₹)
Arithmetic Mean 6 8
Standard Deviation 5 `40/3`

Coefficient of correlation between X and Y is `8/15`. Find

  1. The regression Coefficient of Y on X
  2. The most likely value of Y when X = ₹ 100.
बेरीज
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उत्तर

Given `bar"X"` = 6, `bar"Y"` = 8

σX = 5, σY = `40/3`

and r(X, Y) = `8/15`

Regression coefficient of Y on X

byx = `"r".(sigma_"X")/(sigma_"Y") = 8/15(40/(3 xx 5))`

= `320/225`

= 1.422

byx = 1.422

∴ Regression line of Y on X is

`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`

Y − 8 = 1.422 (X − 6)

Y − 8 = 1.422X − 8.532

Y = 1.422X − 0.532

When X = ₹ 100

Y = 1.422(100) − 0.532

= 142.2 − 0.532

Y = 141.67

∴ When X = ₹ 100, Y = ₹ 141.67

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Regression Analysis
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पाठ 9: Correlation and Regression Analysis - Miscellaneous Problems [पृष्ठ २३०]

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सामाचीर कलवी Business Mathematics and Statistics [English] Class 11 TN Board
पाठ 9 Correlation and Regression Analysis
Miscellaneous Problems | Q 10 | पृष्ठ २३०

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