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प्रश्न
The following results were obtained from records of age (x) and systolic blood pressure (y) of a group of 10 women.
| x | y | |
| Mean | 53 | 142 |
| Variance | 130 | 165 |
`sum(x_i - barx)(y_i - bary)` = 1170
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उत्तर
Here. we need to find line of regressoin of y on x. which is given as:
`bary = "a" + "b"_("y"x)barx`
Where, byx = `("cov"("X", "Y"))/σ_x^2`
= `((sum(x_i - barx)(y_i - bary))/n)/(σ_x^2)`
= `(1170/10)/130` = 0.9
and a = `bary - barb_(yx)barx`
= 142 – (0.9)(53)
= 94.3
Therefore, regression equation of y on x is y = 94.3 + 0.9x
Now, the estimate of blood pressure of women with age 47 years is:
y = 94.3 + 0.9 × 4 7
= 136.6
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| x | y | `x - barx` | `y - bary` | `(x - barx)(y - bary)` | `(x - barx)^2` | `(y - bary)^2` |
| 1 | 5 | – 2 | – 4 | 8 | 4 | 16 |
| 2 | 7 | – 1 | – 2 | `square` | 1 | 4 |
| 3 | 9 | 0 | 0 | 0 | 0 | 0 |
| 4 | 11 | 1 | 2 | 2 | 4 | 4 |
| 5 | 13 | 2 | 4 | 8 | 1 | 16 |
| Total = 15 | Total = 45 | Total = 0 | Total = 0 | Total = `square` | Total = 10 | Total = 40 |
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