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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
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 productivity index of a worker whose test score is 95.
From the following data obtain the equation of two regression lines:
| X | 6 | 2 | 10 | 4 | 8 |
| Y | 9 | 11 | 5 | 8 | 7 |
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 |
Choose the correct alternative.
If u = `("x - a")/"c" and "v" = ("y - b")/"d" "then" "b"_"xy"` = _________
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:
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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 = _______
Corr (x, x) = 1
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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.
‘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
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 ______.
