Advertisements
Advertisements
Question
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).
Advertisements
Solution
| X | Y | X2 | Y2 | XY |
| 1 | 4 | 1 | 16 | 4 |
| 2 | 8 | 4 | 64 | 14 |
| 3 | 2 | 9 | 4 | 6 |
| 4 | 12 | 16 | 144 | 48 |
| 5 | 10 | 25 | 100 | 50 |
| 6 | 14 | 36 | 196 | 84 |
| 7 | 16 | 49 | 256 | 112 |
| 8 | 6 | 64 | 36 | 48 |
| 9 | 18 | 81 | 324 | 162 |
| 45 | 90 | 285 | 1140 | 530 |
N = 9, ΣX = 45, ΣY = 90, ΣX2 = 285, ΣY2 = 1140, ΣXY = 530, `bar"X" = (sum"X")/"N" = 45/9` = 5, `bar"Y" = (sum"Y")/"N" = 90/9` = 10
byx = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"X"^2 - (sum"X")^2)`
= `(9(530) - (45)(90))/(9(285) - (45)^2)`
= `(4770 - 4050)/(2565 - 2025)`
= `720/540`
= 1.33
Regression line of Y on X:
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y – 10 = 1.33 (X – 5)
Y = 1.33X – 6.65 + 10
Y = 1.33X + 3.35
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.
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
If the regression coefficient of Y on X is 2, then the regression coefficient of X on Y is
The term regression was introduced by
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.
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.
