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प्रश्न
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.
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उत्तर
| X = xi | Y = yi | `bb("x"_"i"^2)` | xi yi |
| 1 | 2 | 1 | 2 |
| 2 | 1 | 4 | 2 |
| 3 | 6 | 9 | 18 |
| 6 | 9 | 14 | 22 |
From the table, we have
n = 3, ∑ xi = 6, ∑ yi = 9, `sum "x"_"i"^2 = 14`, ∑ xi yi = 22
`bar x = (sum x_i)/"n" = 6/3 = 2`
`bar y = (sum y_i)/"n" = 9/3 = 3`
Now, `"b"_"YX" = (sum"x"_"i" "y"_"i" - "n" bar "x" bar "y")/(sum "x"_"i"^2 - "n" bar"x"^2)`
`= (22 - 3xx2xx3)/(14 - 3(2)^2)`
`= (22 - 18)/(14 - 12)`
`= 4/2`
= 2
The regression equation of Y on X is,
`(y - bary) = "b"_("YX") (x - barx)`
y − 3 = 2(x − 2)
y − 3 = 2x − 4
y = 2x − 4 + 3
y = 2x − 1 is the regression equation of Y on X. ...(1)
When x = 4, y = ?
Substituting x = 4 in equation (1)
y = 2(4) − 1
= 8 − 1
y = 7
संबंधित प्रश्न
The HRD manager of a company wants to find a measure which he can use to fix the monthly income of persons applying for the job in the production department. As an experimental project, he collected data of 7 persons from that department referring to years of service and their monthly incomes.
| Years of service (X) | 11 | 7 | 9 | 5 | 8 | 6 | 10 |
| Monthly Income (₹ 1000's)(Y) | 10 | 8 | 9 | 5 | 9 | 7 | 11 |
- Find the regression equation of income on years of service.
- What initial start would you recommend for a person applying for the job after having served in a similar capacity in another company for 13 years?
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 |
From the following data estimate y when x = 125.
| X | 120 | 115 | 120 | 125 | 126 | 123 |
| Y | 13 | 15 | 14 | 13 | 12 | 14 |
From the following data obtain the equation of two regression lines:
| X | 6 | 2 | 10 | 4 | 8 |
| Y | 9 | 11 | 5 | 8 | 7 |
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.
Cov (x, y) = __________
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:
There are __________ types of regression equations.
Fill in the blank:
|bxy + byx| ≥ ______
Fill in the blank:
bxy . byx = _______
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.
Corr (x, y) = Corr (y, x)
State whether the following statement is True or False.
bxy and byx are independent of change of origin and scale.
‘r’ is regression coefficient of Y on 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
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 ______.
