Advertisements
Advertisements
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
- The regression Coefficient of Y on X
- The most likely value of Y when X = ₹ 100.
Advertisements
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
APPEARS IN
संबंधित प्रश्न
From the data given below:
| Marks in Economics: | 25 | 28 | 35 | 32 | 31 | 36 | 29 | 38 | 34 | 32 |
| Marks in Statistics: | 43 | 46 | 49 | 41 | 36 | 32 | 31 | 30 | 33 | 39 |
Find
- The two regression equations,
- The coefficient of correlation between marks in Economics and Statistics,
- The mostly likely marks in Statistics when the marks in Economics is 30.
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.
Find the equation of the regression line of Y on X, if the observations (Xi, Yi) are the following (1, 4) (2, 8) (3, 2) (4, 12) (5, 10) (6, 14) (7, 16) (8, 6) (9, 18).
For 5 observations of pairs of (X, Y) of variables X and Y the following results are obtained. ∑X = 15, ∑Y = 25, ∑X2 = 55, ∑Y2 = 135, ∑XY = 83. Find the equation of the lines of regression and estimate the values of X and Y if Y = 8; X = 12.
The regression coefficient of Y on X
When one regression coefficient is negative, the other would be
The lines of regression intersect at the point
The term regression was introduced by
X and Y are a pair of correlated variables. Ten observations of their values (X, Y) have the following results. ∑X = 55, ∑XY = 350, ∑X2 = 385, ∑Y = 55, Predict the value of y when the value of X is 6.
Find the line regression of Y on X
| X | 1 | 2 | 3 | 4 | 5 | 8 | 10 |
| Y | 9 | 8 | 10 | 12 | 14 | 16 | 15 |
