Advertisements
Advertisements
प्रश्न
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 productivity index of a worker whose test score is 95.
Advertisements
उत्तर
Here, X = Aptitude score, Y = Productivity index
| X = xi | Y =yi | `"x"_"i" - bar"x"` | `bar"y"_"i" - bar"y"` | `("x"_"i" - bar"x")^2` | `("y"_"i" - bar"y")^2` | `("x"_"i" - bar"x")("y"_"i" - bar"y")` |
| 60 | 68 | -5 | 3 | 25 | 9 | -15 |
| 62 | 60 | -3 | -5 | 9 | 25 | 15 |
| 65 | 62 | 0 | -3 | 0 | 9 | 0 |
| 70 | 80 | 5 | 15 | 25 | 225 | 75 |
| 72 | 85 | 7 | 20 | 49 | 400 | 140 |
| 48 | 40 | -17 | -25 | 289 | 625 | 425 |
| 53 | 52 | -12 | -13 | 144 | 169 | 156 |
| 73 | 62 | 8 | -3 | 64 | 9 | -24 |
| 65 | 60 | 0 | -5 | 0 | 25 | 0 |
| 82 | 81 | 17 | 16 | 289 | 256 | 272 |
| 650 | 650 | - | - | 894 | 1752 | 1044 |
From the table, we have
n = 10, ∑ xi = 650, ∑ yi = 650
∴ `bar"x" = (sum "x"_"i")/"n" = 650/10 = 65`
`bar"y" = (sum "y"_"i")/"n" = 650/10 = 65`
Since the mean of X and Y are whole numbers, we will use the formula
`"b"_"YX" = (sum ("x"_"i" - bar"x")("y"_"i" - bar"y"))/(sum("x"_"i" - bar"x")^2) and "b"_"XY" = (sum ("x"_"i" - bar"x")("y"_"i" - bar"y"))/(sum("y"_"i" - bar"y")^2)`
From the table, we have
`sum ("x"_"i" - bar"x")("y"_"i" - bar"y") = 1044, sum ("x"_"i" - bar"x")^2 = 894, sum ("y"_"i" - bar"y") = 1752`
`"b"_"YX" = (sum ("x"_"i" - bar"x")("y"_"i" - bar"y"))/(sum("x"_"i" - bar"x")^2) = 1044/894 = 1.16`
Now, `"a" = bar"y" - "b"_"YX" bar"x"`
= 65 - 1.16 × 65 = 65 - 75.4 = - 10.4
∴ The regression equation of productivity index (Y) on Aptitude score (X) is
Y = a + bYX X
∴ Y = - 10.4 + 1.16 X
For X = 95,
Y = - 10.4 + 1.16(95) = - 10.4 + 110.2 = 99.8
∴ The productivity index of worker with a test score of 95 is 99.8.
APPEARS IN
संबंधित प्रश्न
Choose the correct alternative:
There are ______ types of regression equations
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 |
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.
Choose the correct alternative.
If u = `("x - a")/"c" and "v" = ("y - b")/"d" "then" "b"_"yx"` = _________
Choose the correct alternative.
Corr (x, x) = _____
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 u = `"x - a"/"c" and "v" = "y - b"/"d"` then bxy = _______
Fill in the blank:
If u = `"x - a"/"c" and "v" = "y - b"/"d"` then byx = _______
Fill in the blank:
bxy . byx = _______
Corr (x, x) = 1
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 bxy = buv
State whether the following statement is True or False.
If u = x - a and v = y - b then rxy = ruv
State whether the following statement is True or False:
Correlation analysis is the theory of games
If bxy < 0 and byx < 0 then 'r ' is ______.
