Question

1. statistics & probability * which of the following is closest to the slope of the line of best fit (with the least sum of squared residuals) for the data represented by the scatterplot in the standard (x,y) coordinate plane below? a. $\frac{5}{2}$ b. $-\frac{5}{2}$ c. - 1 d. $-\frac{2}{5}$

Explanation:

Step1: Observe the scatter - plot trend

The points in the scatter - plot show a negative linear trend. As \(x\) increases, \(y\) decreases.

Step2: Estimate two points on the line of best - fit

We can roughly estimate two points that the line of best - fit might pass through. Let's assume the line passes through \((5,25)\) and \((20,15)\) (these are estimated based on the general pattern of the scatter - plot).

Step3: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \(x_1 = 5,y_1 = 25,x_2=20,y_2 = 15\) into the formula, we get \(m=\frac{15 - 25}{20 - 5}=\frac{- 10}{15}=-\frac{2}{3}\approx-\frac{2}{5}\) when considering the closest option.

Answer:

D. \(-\frac{2}{5}\)