Financial Risk Manager Part 1

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Given a regression equation is of the form: $y_i = \alpha + \beta x_i$ where Y is the dependent variable (foetal weight), X is the independent variable (gestation period, in weeks), $\alpha =$ the y-intercept, and $\beta =$ the slope.

If $\alpha = -4.60$ and $\beta = 0.2043$ , then estimate the weight of the foetus at exactly 31 weeks.

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TTanishq

1.533kg

1.733kg

1.722kg

1.8kg

Explanation:

Explanation

The regression equation is given as:

$y_i = \alpha + \beta x_i$

Where:

$y_i$ = dependent variable (foetal weight)
$x_i$ = independent variable (gestation period in weeks)
$\alpha = -4.60$ (y-intercept)
$\beta = 0.2043$ (slope)

To estimate the weight at 31 weeks:

$y = -4.60 + 0.2043 \times 31$

Breaking down the calculation:

First, calculate $0.2043 \times 31 = 6.3333$
Then add: $-4.60 + 6.3333 = 1.7333$

Therefore, the estimated weight is 1.733 kg.

This regression model suggests that for each additional week of gestation, the foetal weight increases by approximately 0.2043 kg, starting from a baseline of -4.60 kg at week 0 (which is a theoretical intercept point, not meaningful in practical terms for this context).

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