Advertisements
Advertisements
Question
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.
Advertisements
Solution
Let X represent the marks in subject A and Y represent the marks in subject B.
Given `bar"X"` = 39.5, `bar"Y"` = 47.5
σX = 10.8, σY = 16.8
r(X, Y) = 0.42
∴ Regression coefficient of Y on X
byx = `"r" . (sigma_"Y")/(sigma_"X")`
= `0.42 (16.8/10.8)`
= `7.056/10.8`
= 0.653
∴ Regression line of Y on X is
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y − 47.5 = 0.653 (X − 39.5)
Y − 47.5 = 0.653X − 25.79
Y = 0.653X + 21.71
When X = 52, Y = 0.653(52) + 21.71
Y = 33.956 + 21.71
Y = 55.67
Hence, the estimate of marks in B for the candidate who secured 52 marks in A is 55.67
APPEARS IN
RELATED QUESTIONS
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.
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.
Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480.
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.
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
The term regression was introduced by
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.
