Advertisements
Advertisements
प्रश्न
Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480.
Advertisements
उत्तर
N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480
`bar"X" = (sum"X")/"N" = 80/20` = 4
`bar"Y" - (sum"Y")/"N" = 40/20` = 2
byx = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"X"^2 - (sum"X")^2)`
= `(20(480) - (80)(40))/(20(1680) - (80)^2)`
= `(9600 - 3200)/(33600 - 6400)`
= `6400/27200`
= 0.235
= 0.24
Regression line of Y on X
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y − 2 = 0.24 (X − 4)
Y = 0.24X − 0.96 + 2
Y = 0.24X + 1.04
bxy = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"Y"^2 - (sum"Y")^2)`
= `(20(480) - (80)(40))/(20(320) - (40)^2)`
= `(9600 - 3200)/(6400 - 1600)`
= `6400/4800`
= 1.33
Regression line of X on Y
`"X" - bar"X" = "b"_"xy"("Y" - bar"Y")`
X – 4 = 1.33 (Y – 2)
X = 1.33Y – 2.66 + 4
X = 1.33Y + 1.34
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.
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.
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 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.
The regression coefficient of X on Y
When one regression coefficient is negative, the other would be
If X and Y are two variates, there can be at most
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.
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.
