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Home > Statistical Methods calculators > Find the equation of two regression lines, also estimate calculator
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Method and examples
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Method
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Find the equation of two regression lines, also estimate
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Decimal Place =
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Solution
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Solution provided by AtoZmath.com
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Find the equation of two regression lines, also estimate calculator
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Method-1 :
1. Find the equation of regression lines and estimate y for x = 1 and x for y =4.
| X |
3 |
2 |
-1 |
6 |
4 |
-2 |
5 |
7 |
| Y |
5 |
13 |
12 |
-1 |
2 |
20 |
0 |
-3 |
Method-2 :
1. The regression equation of two variables are 5y = 9x - 22 and 20x = 9y + 350
Find the means of x and y. Also find the value of r.
Method-3 :
1. The following information is obtained form the results of examination
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Marks in Stats |
Marks in Maths |
| Average |
39.5 |
47.5 |
| S.D. |
10.8 |
16.8 |
The correlation coefficient between x and y is 0.42. Obtain two regression lines and estimate y for x = 50 and x for y = 30.
Method-4 :
1. The following information is obtained for two variables x and y. Find the regression equations of y on x.
| `sum XY` = 3467 |
`sum X` = 130 |
`sum X^2` = 2288 |
| n = 10 |
`sum Y` = 220 |
`sum Y^2` = 8822 |
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Example1. Find Regression line equations from the following data
| Class-X | Y | | 2 - 4 | 3 | | 4 - 6 | 4 | | 6 - 8 | 2 | | 8 - 10 | 1 |
Solution:| Class-X | Mid value `x` | `y` | `x^2` | `y^2` | `x*y` | | 2 - 4 | 3 | 3 | 9 | 9 | 9 | | 4 - 6 | 5 | 4 | 25 | 16 | 20 | | 6 - 8 | 7 | 2 | 49 | 4 | 14 | | 8 - 10 | 9 | 1 | 81 | 1 | 9 | | --- | --- | --- | --- | --- | --- | | | `sum x=24` | `sum y=10` | `sum x^2=164` | `sum y^2=30` | `sum xy=52` |
Mean `bar x = (sum x)/n` `=24/4` `=6` Mean `bar y = (sum y)/n` `=10/4` `=2.5` `byx = (n sum xy - (sum x)(sum y))/(n sum x^2 - (sum x)^2)` `=(4 * 52 - 24 * 10 )/(4 * 164 - (24)^2)` `=(208 - 240 )/(656 - 576)` `=-32/80` `=-0.4` Regression Line y on x `y - bar y = byx (x - bar x)` `y - 2.5 = -0.4 (x - 6)` `y - 2.5 = -0.4 x + 2.4` `y = -0.4 x + 2.4 + 2.5` `y = -0.4 x + 4.9` `bxy = (n sum xy - (sum x)(sum y))/(n sum y^2 - (sum y)^2)` `=(4 * 52 - 24 * 10 )/(4 * 30 - (10)^2)` `=(208 - 240 )/(120 - 100)` `=-32/20` `=-1.6` Regression Line x on y `x - bar x = bxy (y - bar y)` `x - 6 = -1.6 (y - 2.5)` `x - 6 = -1.6 y + 4` `x = -1.6 y + 4 + 6` `x = -1.6 y + 10`
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