Financial Risk Manager Part 1

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Explanation:

First, we need to estimate regression coefficients.

b_1 = \frac{\text{Cov}(X, Y)}{\text{Var}(X)} = \frac{\sum (X_i - \bar{X}) \times (Y_i - \bar{Y})}{\sum (X_i - \bar{X})^2} = \frac{2}{320} = 0.00625

b_0 = \bar{Y} - b_1 \times \bar{X} = 1,011.40 - 0.00625 \times 2,637 = 995

The equation of regression line is

y = 995 + 0.00625x

Close Price	Y (GOOG)	X (S&P)	$Y_i - \bar{Y}$	$X_i - \bar{X}$	$(X_i - \bar{X}) \times (Y_i - \bar{Y})$	$(X_i - \bar{X})^2$
Dec 05, 2017	1,005	2,630	$-6.4$	$-7$	44.8	49
Dec 04, 2017	999	2,639	$-12.4$	2	$-24.8$	4
Dec 01, 2017	1,010	2,642	$-1.4$	5	$-7$	25
Nov 30, 2017	1,021	2,648	9.6	11	105.6	121
Nov 29, 2017	1,022	2,626	10.6	$-11$	$-116.6$	121
Sum	5,057	13,185	0	0	2	320
Average	1,011.40	2,637

Explanation:

First, we need to estimate regression coefficients.

b_1 = \frac{\text{Cov}(X, Y)}{\text{Var}(X)} = \frac{\sum (X_i - \bar{X}) \times (Y_i - \bar{Y})}{\sum (X_i - \bar{X})^2} = \frac{2}{320} = 0.00625

b_0 = \bar{Y} - b_1 \times \bar{X} = 1,011.40 - 0.00625 \times 2,637 = 995

The equation of regression line is

y = 995 + 0.00625x

Close Price	Y (GOOG)	X (S&P)	$Y_i - \bar{Y}$	$X_i - \bar{X}$	$(X_i - \bar{X}) \times (Y_i - \bar{Y})$	$(X_i - \bar{X})^2$
Dec 05, 2017	1,005	2,630	$-6.4$	$-7$	44.8	49
Dec 04, 2017	999	2,639	$-12.4$	2	$-24.8$	4
Dec 01, 2017	1,010	2,642	$-1.4$	5	$-7$	25
Nov 30, 2017	1,021	2,648	9.6	11	105.6	121
Nov 29, 2017	1,022	2,626	10.6	$-11$	$-116.6$	121
Sum	5,057	13,185	0	0	2	320
Average	1,011.40	2,637

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UAnonymous

Last updated: May 21, 2026 at 04:19

$y = 995 + 0.00625x$

$y = 574 + 0.859x$

$y = 0.859 + 574x$

$y = 989 + 0.859x$