Question

the length (in inches) and weight (in ounces) for a type of bass were measured for a random sample of 10 bass from a lake. the measurements are given in the table.
length (x) 11 14.75 10.75 9.5 13.75 9.5 10.25 10.5 8 8.25
weight (y) 16 30 15 11 30 9 12 14 8 7
using technology, what is the value of ( r^{2} )?
-0.98
-0.96
0.96
0.98

Explanation:

Step1: Input data into technology

Input the length (\(x\)) and weight (\(y\)) data into a statistical software or calculator (e.g., TI - 84: STAT → EDIT to enter data, then STAT → CALC → LinReg(ax + b)).

Step2: Find the correlation coefficient \(r\)

After running the linear regression, the calculator will give the value of \(r\) (the correlation coefficient).

Step3: Calculate \(r^{2}\)

Square the value of \(r\). Since the relationship between length and weight is positive (as length increases, weight generally increases), \(r\) is positive. If \(r\approx0.98\), then \(r^{2}=(0.98)^{2}=0.9604\approx0.96\)

Answer:

0.96