Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
N = 5, ΣX = 15, ΣY = 25, ΣX2 = 55, ΣY2 = 135, ΣXY = 83, `bar"X" = 15/5` = 3, `bar"Y" = 25/5` = 5.
byx = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"(sum"X"^2) - (sum"X")^2)`
= `(5(83) - (15)(25))/(5(55) - (15)^2)`
= `(415 - 375)/(275 - 225)`
= `40/50`
= 0.8
Regression line of Y on X:
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y – 5 = 0.8(X – 3)
Y = 0.8X – 2.4 + 5
Y = 0.8X + 2.6
When X = 12, Y = 0.8X + 2.6
Y = (0.8)12 + 2.6
= 9.6 + 2.6
= 12.2
bxy = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"(sum"Y"^2) - (sum"Y")^2)`
= `(5(83) - (15)(25))/(5(135) - (25)^2)`
= `(415 - 375)/(675 - 625)`
= `40/50`
= 0.8
Regression line of X on Y:
`"X" - bar"X" = "b"_"xy"("Y" - bar"Y")`
X – 3 = 0.8(Y – 5)
X = 0.8Y – 4 + 3
X = 0.8Y – 1
When Y = 8, X = 0.8Y – 1
X = (0.8)8 – 1
= 6.4 – 1
= 5.4
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.
Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480.
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
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
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.
Using the following information you are requested to
- obtain the linear regression of Y on X
- Estimate the level of defective parts delivered when inspection expenditure amounts to ₹ 82
∑X = 424, ∑Y = 363, ∑X2 = 21926, ∑Y2 = 15123, ∑XY = 12815, N = 10.
Here X is the expenditure on inspection, Y is the defective parts delivered.
