Question

Given the data set (4, 85), (7, 92), (14, 110), which of the following equations best represents a line of best fit?

Answer 1

Let's see if there is a constant rate first...

(92-85)/(7-4)=7/3

(110-92)/(14-7)=18/7  so there is no constant rate...so the line of best fit (linear least squares regression line) will have a slope of:

m=(nΣxy-ΣxΣy)/(nΣx^2-ΣxΣx)

m=(3*2524-25*287)/(3*261-625)

m=397/158

b=(Σy-mΣx)/n

b=(158Σy-397Σx)/(3*158)

b=(45346-9925)/(3*158)

b=11807/158

So the line of best fit is:

y=(397x+11807)/158

so approximating this line....

y≈2.5x+74.73

So the closest that you have is:

y=7x/3+75.67

Answer 2

Answer A should be the correct answer