Skin Diver and Scuba News published some data on shark body length (feet) and ja
ID: 3024241 • Letter: S
Question
Skin Diver and Scuba News published some data on shark body length (feet) and jaw width (inches) for n = 44 sharks. For this sample, the mean body length = 15.586 ft (x -bar) ; sx = 2.551. The mean jaw width = 15.705 inches (y-bar) ; sy = 2.800. The correlation coefficient is r = 0.8749.
Which equation below is the equation of least squares regression line that can be used to predict jaw width from body length, i.e., the regression line of jaw width on body length?
jaw width = 0.74 + 0.96 X length
jaw width = 0.51 + 0.96 X length
jaw width = 3.4 + 0.79 X length
jaw width = - 3.4 + 0.79 X length
a.jaw width = 0.74 + 0.96 X length
b.jaw width = 0.51 + 0.96 X length
c.jaw width = 3.4 + 0.79 X length
d.jaw width = - 3.4 + 0.79 X length
Explanation / Answer
x=body length
predict y=jaw width
y = intercept + slope x
slope=r · (SD of y) / (SD of x )
slope= 0.8749 * (2.808) / 2.551=0.9630416
for each extra ft body length is worth 0.96 inches in jaw width.
The intercept of the regression line is predicted value for y, when x=0.
when x=0 it is 15.586 below average
using the slope we can predict below average by 0.96(15.586)=14.96256
so jaw size is 15.705-14.96256=0.74
jaw width = 0.74 + 0.96 X length
jaw width = 0.74 + 0.96 X length
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