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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
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 |
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| 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 |
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.
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Corr (x, x) = _____
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byx = ______
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bxy = ______
Choose the correct alternative.
Cov (x, y) = __________
Choose the correct alternative.
If bxy < 0 and byx < 0 then 'r' is __________
Fill in the blank:
If bxy < 0 and byx < 0 then ‘r’ is __________
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Regression equation of Y on X is_________
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If u = `"x - a"/"c" and "v" = "y - b"/"d"` then bxy = _______
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|bxy + 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.
‘r’ is regression coefficient of Y on X
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 |
