Question

data set a can be written as y = -5.6 + 8.8x, where 2 ≤ x ≤ 6. the puppy was weighed again at 9 months old and weighed 52 pounds. data set b consists of all the data points in data set a as well as the data point (9, 52). the equation of a line of best fit for data set b can be written as y = r + sx, where r and s are a 5.9 b 8.8 c 14.4 d 17.8

Explanation:

Step1: Recall the concept of slope change in linear regression

Adding an out - of - range data point can change the slope of the line of best fit.

Step2: Analyze the new data point

The new data point is $(9,52)$. For data set A, the equation is $y=-5.6 + 8.8x$ with $2\leq x\leq6$. The $x$ - value of the new point ($x = 9$) is outside the original range.

Step3: Understand the impact on slope

When we add a new data point, we can use the formula for the slope of the line of best fit in a more general sense. But an intuitive way is to consider the position of the point. If we assume the original line $y=-5.6 + 8.8x$, when $x = 9$, $y=-5.6+8.8\times9=-5.6 + 79.2 = 73.6$. The actual $y$ - value of the new point is $52$. This new point will pull the line downwards, decreasing the slope. Since the original slope is $8.8$, the new slope $s$ must be less than $8.8$.

Step4: Check the options

Among the options A. $5.9$, B. $8.8$, C. $14.4$, D. $17.8$, the only value less than $8.8$ is $5.9$.

Answer:

A. $5.9$