To calculate the regression line $y = a + bx$, let $x$ be the S&P 500 index prices and $y$ be the GOOG prices.

First, calculate the means ($\bar{x}$ and $\bar{y}$): $\bar{x} = \frac{2630 + 2639 + 2642 + 2648 + 2626}{5} = 2637$ $\bar{y} = \frac{1005 + 999 + 1010 + 1021 + 1022}{5} = 1011.4$

Next, calculate the slope $b = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$ Deviations for $x$ ($x_i - \bar{x}$): -7, 2, 5, 11, -11 Deviations for $y$ ($y_i - \bar{y}$): -6.4, -12.4, -1.4, 9.6, 10.6

Covariance term (Numerator): $(-7)(-6.4) + (2)(-12.4) + (5)(-1.4) + (11)(9.6) + (-11)(10.6)$ $= 44.8 - 24.8 - 7 + 105.6 - 116.6 = 2.0$

Variance term (Denominator): $(-7)^2 + 2^2 + 5^2 + 11^2 + (-11)^2 = 49 + 4 + 25 + 121 + 121 = 320$

Slope $b = \frac{2.0}{320} = 0.00625$

Finally, calculate the intercept $a = \bar{y} - b\bar{x}$: $a = 1011.4 - 0.00625 \times 2637 = 1011.4 - 16.48 = 994.92 \approx 995$

The resulting regression equation is $y = 995 + 0.00625x$.