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प्रश्न
The equations of two lines of regression obtained in a correlation analysis are the following 2X = 8 – 3Y and 2Y = 5 – X. Obtain the value of the regression coefficients and correlation coefficients.
उत्तर
Let regression line of Y on X be,
2Y = 5 – X
Y = – 0.5X + 2.5
byx = – 0.5
i.e., byx = `-1/2`
Let regression line of X on Y be
2X = 8 – 3Y
X = – 1.5Y + 4
bxy = – 1.5
i.e., bxy = `-3/2`
Correlation coefficient (r) = `± sqrt("b"_"xy" xx "b"_"yx")`
= `± sqrt(1.5 xx 0.5)`
= – 0.866
Both bxy and byx is negative so take a negative sign.
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संबंधित प्रश्न
From the data given below:
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| Marks in Statistics: | 43 | 46 | 49 | 41 | 36 | 32 | 31 | 30 | 33 | 39 |
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| X | 61 | 68 | 68 | 64 | 65 | 70 | 63 | 62 | 64 | 67 |
| Y | 112 | 123 | 130 | 115 | 110 | 125 | 100 | 113 | 116 | 125 |
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| Details | Rainfall | Production |
| Mean | 25`` | 40 units per acre |
| Standard Deviation | 3`` | 6 units per acre |
Coefficient of correlation between rainfall and production is 0.8.
You are given the following data:
| Details | X | Y |
| Arithmetic Mean | 36 | 85 |
| Standard Deviation | 11 | 8 |
If the Correlation coefficient between X and Y is 0.66, then find
- the two regression coefficients,
- the most likely value of Y when X = 10.
The regression coefficient of X on Y
When one regression coefficient is negative, the other would be
The lines of regression of X on Y estimates
The lines of regression intersect at the point
Using the following information you are requested to
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Here X is the expenditure on inspection, Y is the defective parts delivered.
