Question

The table below shows randy breuers height in inches leading into his teen years. The graph below displays a scatter plot of the data. Which equation best represents the line of best fit for this data?
The choices are:
A. y=1.1x+23
B. y=1.25x+20
C. y=1.25x+40.67
D. y=1.4x+40.67

Answer 1

The least-square regression line has a slope of:

m=(nΣxy-ΣyΣx)/(nΣx²-ΣxΣx)

and a y-intercept of:

b=(Σy-mΣx)/n

In this case: n=7, Σxy=4899, Σy=391, Σx=85, Σx²=1153 so

m=(7(4899)-391*85)/(7(1153)-85*85))=1058/846

b=(391*846-85*1058)/(7*846)=34408/846

So the line of best fit is:

y=(1058x+34408)/846  and if we approximated this as your answers see to have done....

y=1.25x+40.67