Advertisements
Advertisements
Question
Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480.
Advertisements
Solution
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
RELATED QUESTIONS
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.
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.
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).
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.
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.
If X and Y are two variates, there can be at most
The lines of regression of X on Y estimates
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.
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.
