Advertisements
Advertisements
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.
उत्तर
| Marks in Economics (X) | Marks in Statistics (Y) | x = `"X" - bar"X"` | y = `"Y" - bar"Y"` | x2 | y2 | xy |
| 25 | 43 | − 7 | 5 | 49 | 25 | − 35 |
| 28 | 46 | − 4 | 8 | 16 | 64 | − 32 |
| 35 | 49 | 3 | 11 | 9 | 121 | 33 |
| 32 | 41 | 0 | 3 | 0 | 9 | 0 |
| 31 | 36 | − 1 | − 2 | 1 | 4 | 2 |
| 36 | 32 | 4 | − 6 | 16 | 36 | − 24 |
| 29 | 31 | − 3 | − 7 | 9 | 49 | 21 |
| 38 | 30 | 6 | − 8 | 36 | 64 | − 48 |
| 34 | 33 | 2 | − 5 | 4 | 25 | − 10 |
| 32 | 39 | 0 | 1 | 0 | 1 | 0 |
| 320 | 380 | 0 | 0 | 140 | 398 | − 93 |
N = 10, ∑X = 320, ∑Y = 280, ∑x2 = 140, ∑y2 = 398, ∑xy = − 93, `bar"X" = 320/100` = 32, `bar"Y" = 380/100` = 38
(a) Regression equation of X on Y.
bxy = `"r"(sigma_"x")/(sigma_"y") = (sum"xy")/(sum"y"^2) = (-93)/398` = − 0.234
`"X" - bar"X" = "b"_"xy"("Y" - bar"Y")`
X − 32 = − 0.234(Y − 38)
X = − 0.234Y + 8.892 + 32
X = − 0.234Y + 40.892
Regression equation of Y on X.
`"Y" - bar"Y" = "b"_"xy"("X" - bar"X")`
byx = `"r"(sigma_"x")/(sigma_"y") = (sum"xy")/(sum"y"^2) = (-93)/140` = − 0.664
Y − 38 = − 0.664(X − 32)
Y = − 0.664X + 21.248 + 38
Y = − 0.664X + 59.248
(b) Coefficient of correlation (r) = `±sqrt("b"_"xy" xx "b"_"yx")`
= `sqrt((-0.234)(-0.664))`
= − 0.394
(c) When X = 30, Y = ?
Y = − 0.664(30) + 59.248
= − 19.92 + 59.248
= 39.328
APPEARS IN
संबंधित प्रश्न
The heights (in cm.) of a group of fathers and sons are given below:
| Heights of fathers: | 158 | 166 | 163 | 165 | 167 | 170 | 167 | 172 | 177 | 181 |
| 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.
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.
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 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 X on Y
The regression coefficient of Y on X
When one regression coefficient is negative, the other would be
The following data pertains to the marks in subjects A and B in a certain examination. Mean marks in A = 39.5, Mean marks in B = 47.5 standard deviation of marks in A = 10.8 and Standard deviation of marks in B = 16.8. coefficient of correlation between marks in A and marks in B is 0.42. Give the estimate of marks in B for the candidate who secured 52 marks in A.
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.
