Finding a Best Fit Line, Help?

Question

anonymous · Answer

I dont understand the topic?

mimi_x3 · Answer

Lols, whats the question ?

anonymous · Answer

(10, 150)  (20, 275)  (30, 340)  (40, 400)  (50, 475)

Title: Intersection Cars
Horizontal axis: Minutes elapsed
Vertical axis: Total cars passing through

anonymous · Answer

Thats Question 1

valpey · Answer

If it is total cars passing through, these are not independent data points. You will have to take the difference between successive data points. i.e. 150, 125, 65, 60, 75 to get number of cars per ten minutes. Then your best fit line might behave like an ordinary least squares line.

anonymous · Answer

For problems 1 and 2, graph the data points. Draw the line of best fit and, using complete sentences, explain how you found it in 3-4 sentences. Write the equation for the line of best fit in standard form.

I graphed it, but i dont know how to find the line of best fit...

valpey · Answer

Pretty sure this is the same as the arithmetic average of those five numbers.
$$f(x) = (150-x)^2+(125-x)^2+(65-x)^2+(60-x)^2+(75-x)^2$$
$$f(x) = 150^2+125^2+65^2+60^2+75^2 -2(150+125+65+60+75)x + 5x^2$$
$$f'(x) = -2(150+125+65+60+75) + 10x = 0$$
$$x = (150+125+65+60+75)/5$$

valpey · Answer

Then the line is 
$$TotalCars = Minutes*(150+125+65+60+75)/50$$

anonymous · Answer

where did you get 150, 125, 65,60,75?

valpey · Answer

150 = 150, 125 = 275-150, 65 = 340-275, 60 = 400-340 75 = 475-400

anonymous · Answer

http://mathbits.com/mathbits/tisection/statistics1/linefit.htm

anonymous · Answer

I see... thank you