Given the data set (4, 85), (7, 92), (14, 110), which of the following equations best represents a line of best fit?
2 answers:
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 A should be the correct answer
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