Final answer:
The sum of the squared residuals for the line that contains the points (-2, -4) and (2, 5) is actually 0 because both points lie exactly on the line, resulting in no residuals.
Step-by-step explanation:
The question asks us to find the sum of the squared residuals for the line that passes through the points (-2, -4) and (2, 5). To do this, we must first calculate the equation of the line using the two points. Afterwards, we will be able to compute the residuals for each point. To find the equation of the line, we will use the slope formula, which is (y2 - y1) / (x2 - x1). Calculating the slope, m, gives us (5 - (-4)) / (2 - (-2)) = 9 / 4. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. Using one of the points (-2, -4), we can find b: -4 = (9/4)(-2) + b => -4 = -9/2 + b => b = -8/2 + 9/2 => b = 1/2. So, the equation of our line is y = (9/4)x + 1/2.
Next, we will find the residual for each point by taking the actual y-value minus the y-value predicted by the line. Residuals are: For (-2, -4): -4 - [(-2)(9/4) + 1/2] = -4 - (-4.5 + 0.5) = -4 + 4 = 0. For (2, 5): 5 - [(2)(9/4) + 1/2] = 5 - (4.5 + 0.5) = 5 - 5 = 0. Since the points lie exactly on the line, the residuals are 0. The sum of the squared residuals is therefore 0^2 + 0^2 = 0, which is not one of the provided options. This indicates there might be an error in the question or the provided options. Normally, the sum of squared residuals is used to measure how well a regression line fits a set of points, but in this case, the line fits the points perfectly, resulting in no residuals.