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Explanation:

Step1: Recall the formula for the least - squares regression line

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In a least - squares regression, we can use a statistical software or a calculator with regression capabilities. However, we can also make an estimate by using the fact that for a set of points $(x_i,y_i)$, the slope $m=\frac{n\sum_{i = 1}^{n}x_iy_i-\sum_{i = 1}^{n}x_i\sum_{i = 1}^{n}y_i}{n\sum_{i = 1}^{n}x_i^{2}-(\sum_{i = 1}^{n}x_i)^{2}}$ and the y - intercept $b=\bar{y}-m\bar{x}$, where $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$ and $\bar{y}=\frac{\sum_{i = 1}^{n}y_i}{n}$, and $n$ is the number of data points. Here $n = 6$, $\sum_{i=1}^{6}x_i=-5 + 1+4-8 + 0+9=1$, $\sum_{i=1}^{6}y_i=0-3 + 5-6 + 2+6=4$, $\sum_{i=1}^{6}x_i^{2}=25 + 1+16 + 64+0 + 81=187$, $\sum_{i=1}^{6}x_iy_i=0-3 + 20 + 48+0 + 54=119$.

Step2: Calculate the slope $m$

$m=\frac{6\times119-1\times4}{6\times187 - 1^{2}}=\frac{714 - 4}{1122-1}=\frac{710}{1121}\approx0.63$.

Step3: Calculate the y - intercept $b$

$\bar{x}=\frac{1}{6}\approx0.17$, $\bar{y}=\frac{4}{6}\approx0.67$, $b=\bar{y}-m\bar{x}\approx0.67-0.63\times0.17\approx0.67 - 0.11=0.56\approx0.6$.

Answer:

A. $y = 0.6x+0.6$