Advertisements
Advertisements
प्रश्न
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 |
Advertisements
उत्तर
Since X is independent and Y is dependent variable, we find the regression equation of Y on X.
| X = xi | Y = yi | `"x"_"i"^2` | xi yi |
| 2 | 18 | 4 | 36 |
| 4 | 12 | 16 | 48 |
| 5 | 10 | 25 | 50 |
| 6 | 8 | 36 | 48 |
| 8 | 7 | 64 | 56 |
| 11 | 5 | 121 | 55 |
| 36 | 60 | 266 | 293 |
From the table, we have,
n = 6, ∑ xi = 36, ∑ yi = 60, `sum "x"_"i"^2 = 266`, ∑ xi yi = 293
`bar"x" = (sum "x"_"i")/"n" 36/6 = 6`
`bar"y" = (sum "y"_"i")/"n" = 60/6 = 10`
Now, `"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (293 - 6xx6xx10)/(266 - 6(6)^2) = (293 - 360)/(266 - 216) = (-67)/50`
∴ bYX = - 1.34
Also, `"a"' = bar"y" - "b"_"YX" bar"x"`
= 10 - (- 1.34)(6) = 10 + 8.04 = 18.04
The regression equation of Y on X is
Y = a + bYX X
∴ Y = 18.04 - 1.34 X
APPEARS IN
संबंधित प्रश्न
Choose the correct alternative:
There are ______ types of regression equations
From the following data estimate y when x = 125.
| X | 120 | 115 | 120 | 125 | 126 | 123 |
| Y | 13 | 15 | 14 | 13 | 12 | 14 |
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.
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 |
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"_"xy"` = _________
Choose the correct alternative.
If equations of regression lines are 3x + 2y − 26 = 0 and 6x + y − 31 = 0 then means of x and y are __________
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:
Corr (x, −x) = __________
Fill in the blank:
|bxy + byx| ≥ ______
Fill in the blank:
If byx > 1 then bxy is _______
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.
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
Compute the appropriate regression equation for the following data:
| x (Dependent Variable) | 10 | 12 | 13 | 17 | 18 |
| y (Independent Variable) | 5 | 6 | 7 | 9 | 13 |
If bxy < 0 and byx < 0 then 'r ' is ______.
