Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
To get mean values we must solve the given lines.
4X – 5Y = – 33 ……(1)
20X – 9Y = 107 …….(2)
Equation (1) × 5
20X – 25Y = – 165
20X – 9Y = 107
Subtracting (1) and (2),
– 16Y = – 272
Y = `272/16` = 17
i.e., `bar"Y"` = 17
Using Y = 17 in (1) we get,
4X – 85 = – 33
4X = 85 – 33
4X = 52
X = 13
i.e., `bar"X"` = 13
Mean values are `bar"X"` = 13, `bar"Y"` = 17,
Let regression line of Y on X be
4X – 5Y + 33 = 0
5Y = 4X + 33
Y = `1/5` (4X + 33)
Y = `4/5"X" + 33/5`
Y = 0.8X + 6.6
∴ byx = 0.8
Let regression line of X on Y be
20X – 9Y – 107 = 0
20X = 9Y + 107
X = `1/20` (9Y + 107)
X = `9/20"Y" + 107/20`
X = 0.45Y + 5.35
∴ bxy = 0.45
Coefficient of correlation between X and Y is
r = `± sqrt("b"_"yx" xx "b"_"xy")`
r = `± (0.8 xx 0.45)`
= ± 0.6
= 0.6
Both byx and bxy is positive take positive sign.
APPEARS IN
संबंधित प्रश्न
Given the following data, what will be the possible yield when the rainfall is 29.
| 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.
The following data relate to advertisement expenditure (in lakh of rupees) and their corresponding sales (in crores of rupees)
| Advertisement expenditure | 40 | 50 | 38 | 60 | 65 | 50 | 35 |
| Sales | 38 | 60 | 55 | 70 | 60 | 48 | 30 |
Estimate the sales corresponding to advertising expenditure of ₹ 30 lakh.
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.
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 X on Y
When one regression coefficient is negative, the other would be
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 |
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.
