Advertisements
Advertisements
प्रश्न
Calculate the regression equations of X on Y and Y on X from the following data:
| X | 10 | 12 | 13 | 17 | 18 |
| Y | 5 | 6 | 7 | 9 | 13 |
Advertisements
उत्तर
| X = xi | Y = yi | `"x"_"i"^2` | `"y"_"i"^2` | xi yi |
| 10 | 5 | 100 | 25 | 50 |
| 12 | 6 | 144 | 36 | 72 |
| 13 | 7 | 169 | 49 | 91 |
| 17 | 9 | 289 | 81 | 153 |
| 18 | 13 | 324 | 169 | 234 |
| 70 | 40 | 1026 | 360 | 600 |
From the table, we have,
n = 5, ∑ xi = 70, ∑ yi = 40, ∑ xi yi = 600, `sum"x"_"i"^2 = 1026`, `sum"y"_"i"^2 = 360
`bar"x" = sum"x"_"i"/"n" = 70/5 = 14`,
`bar"y" = sum"y"_"i"/"n" = 40/5 = 8`
Now, for regression equation of X on Y
`"b"_"XY" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "y"_"i"^2 - "n" bar"y"^2)`
`= (600 - 5 xx 14 xx 8)/(360 - 5(8)^2) = (600 - 560)/(360 - 320) = 40/40 = 1`
Also, `"a"' = bar"x" - "b"_"XY" bar"y" = 14 - 1(8) = 14 - 8 = 6`
∴ The regression equation of X on Y is
X = a' + bXYY
∴ X = 6 + Y
Now, for regression equation of Y on X
`"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (600 - 5(14)(8))/(1026 - 5(14)^2) = (600- 560)/(1026 - 980) = 40/46 = 0.87`
Also, a = `bar"y" - "b"_"YX" bar"x"`
`= 8 - 0.87 xx 14 = 8 - 12.18 = - 4.18`
∴ The regression equation of Y on X is
Y = a + bYX X
∴ Y = - 4.18 + 0.87X
APPEARS IN
संबंधित प्रश्न
Choose the correct alternative:
There are ______ types of regression equations
The following table gives the aptitude test scores and productivity indices of 10 workers selected at random.
| Aptitude score (X) | 60 | 62 | 65 | 70 | 72 | 48 | 53 | 73 | 65 | 82 |
| Productivity Index (Y) | 68 | 60 | 62 | 80 | 85 | 40 | 52 | 62 | 60 | 81 |
Obtain the two regression equations and estimate the test score when the productivity index is 75.
Compute the appropriate regression equation for the following data:
| X [Independent Variable] |
2 | 4 | 5 | 6 | 8 | 11 |
| Y [dependent Variable] | 18 | 12 | 10 | 8 | 7 | 5 |
The following are the marks obtained by the students in Economics (X) and Mathematics (Y)
| X | 59 | 60 | 61 | 62 | 63 |
| Y | 78 | 82 | 82 | 79 | 81 |
Find the regression equation of Y on X.
From the following data obtain the equation of two regression lines:
| X | 6 | 2 | 10 | 4 | 8 |
| Y | 9 | 11 | 5 | 8 | 7 |
For the following data, find the regression line of Y on X
| X | 1 | 2 | 3 |
| Y | 2 | 1 | 6 |
Hence find the most likely value of y when x = 4.
From the following data, find the regression equation of Y on X and estimate Y when X = 10.
| X | 1 | 2 | 3 | 4 | 5 | 6 |
| Y | 2 | 4 | 7 | 6 | 5 | 6 |
The following sample gives the number of hours of study (X) per day for an examination and marks (Y) obtained by 12 students.
| X | 3 | 3 | 3 | 4 | 4 | 5 | 5 | 5 | 6 | 6 | 7 | 8 |
| Y | 45 | 60 | 55 | 60 | 75 | 70 | 80 | 75 | 90 | 80 | 75 | 85 |
Obtain the line of regression of marks on hours of study.
Choose the correct alternative.
If u = `("x - a")/"c" and "v" = ("y - b")/"d" "then" "b"_"yx"` = _________
Choose the correct alternative.
Corr (x, x) = _____
The regression equation of y on x is given by 3x + 2y − 26 = 0. Find byx.
Choose the correct alternative.
bxy = ______
Choose the correct alternative.
Cov (x, y) = __________
Fill in the blank:
If bxy < 0 and byx < 0 then ‘r’ is __________
Fill in the blank:
Regression equation of Y on X is_________
Fill in the blank:
There are __________ types of regression equations.
Fill in the blank:
If byx > 1 then bxy is _______
Fill in the blank:
bxy . byx = _______
Corr (x, x) = 1
Regression equation of X on Y is `("y" - bar "y") = "b"_"yx" ("x" - bar "x")`
State whether the following statement is True or False.
Regression equation of Y on X is `("y" - bar "y") = "b"_"yx" ("x" - bar "x")`
State whether the following statement is True or False.
bxy and byx are independent of change of origin and scale.
State whether the following statement is True or False.
byx is correlation coefficient between X and Y
State whether the following statement is True or False.
If u = x - a and v = y - b then rxy = ruv
If bxy < 0 and byx < 0 then 'r ' is ______.
