A wildlife biologist has spent the past 5 years studying the relationship between the length (inches)and the average weight (lb)of the striped bass.His results are summarized in the table below. $$\begin{array} { | l | l | }
\hline \begin{array} { l }
\text { Length } \
\text { (inches) }
\end{array} & \begin{array} { l }
\text { Weight } \
\text { (lb) }
\end{array} \
\hline 14 & 3 \
18 & 6 \
22 & 11 \
26 & 14 \
\hline
\end{array}$$
Find the least squares regression line y = ax + b for the data in the table,where x represents the length of the fish in inches and y represents the weight in pounds.Use this regression line to estimate the average weight of a striped bass that is 21 inches in length.
A)y = 0.85(21)- 12.5 = 5.35 lb
B)y = 0.95(21)- 10.5 = 9.45 lb
C)y = 0.95(21)- 8.5 = 11.45 lb
D)y = 0.75(21)- 9.5 = 6.25 lb
E)y = 0.65(21)- 10.5 = 3.15 lb

Question

A wildlife biologist has spent the past 5 years studying the relationship between the length (inches)and the average weight (lb)of the striped bass.His results are summarized in the table below. $$\begin{array} { | l | l | } 
\hline \begin{array} { l } 
\text { Length } \
\text { (inches) }
\end{array} & \begin{array} { l } 
\text { Weight } \
\text { (lb) }
\end{array} \
\hline 14 & 3 \
18 & 6 \
22 & 11 \
26 & 14 \
\hline
\end{array}$$
Find the least squares regression line y = ax + b for the data in the table,where x represents the length of the fish in inches and y represents the weight in pounds.Use this regression line to estimate the average weight of a striped bass that is 21 inches in length.
A)y = 0.85(21)- 12.5 = 5.35 lb
B)y = 0.95(21)- 10.5 = 9.45 lb
C)y = 0.95(21)- 8.5 = 11.45 lb
D)y = 0.75(21)- 9.5 = 6.25 lb
E)y = 0.65(21)- 10.5 = 3.15 lb

Quizplus · Accepted Answer

Using a graphing calculator or statistical software, we can find that the slope of the least squares regression line (a) is approximately 0.95 and the y-intercept (b) is approximately -10.5. Therefore, the equation of the line is:

y = 0.95x - 10.5

To estimate the weight of a striped bass that is 21 inches in length, we substitute x = 21 into the equation and solve for y:

y = 0.95(21) - 10.5 = 9.45 lb

Therefore, the best choice is B, which gives the estimated weight of a striped bass that is 21 inches in length as 9.45 lb.

A Wildlife Biologist Has Spent the Past 5 Years Studying