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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.
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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
The heights (in cm.) of a group of fathers and sons are given below:
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| Heights of Sons: | 163 | 158 | 167 | 170 | 160 | 180 | 170 | 175 | 172 | 175 |
Find the lines of regression and estimate the height of the son when the height of the father is 164 cm.
The following data give the height in inches (X) and the weight in lb. (Y) of a random sample of 10 students from a large group of students of age 17 years:
| X | 61 | 68 | 68 | 64 | 65 | 70 | 63 | 62 | 64 | 67 |
| Y | 112 | 123 | 130 | 115 | 110 | 125 | 100 | 113 | 116 | 125 |
Estimate weight of the student of a height 69 inches.
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
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- the most likely value of Y when X = 10.
A survey was conducted to study the relationship between expenditure on accommodation (X) and expenditure on Food and Entertainment (Y) and the following results were obtained:
| Details | Mean | SD |
| Expenditure on Accommodation (₹) | 178 | 63.15 |
| Expenditure on Food and Entertainment (₹) | 47.8 | 22.98 |
| Coefficient of Correlation | 0.43 | |
Write down the regression equation and estimate the expenditure on Food and Entertainment, if the expenditure on accommodation is ₹ 200.
The two regression lines were found to be 4X – 5Y + 33 = 0 and 20X – 9Y – 107 = 0. Find the mean values and coefficient of correlation between X and Y.
The regression coefficient of Y on X
When one regression coefficient is negative, the other would be
If the regression coefficient of Y on X is 2, then the regression coefficient of X on Y is
The lines of regression intersect at the point
Using the following information you are requested to
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- Estimate the level of defective parts delivered when inspection expenditure amounts to ₹ 82
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Here X is the expenditure on inspection, Y is the defective parts delivered.
