+0

# Line of best fit

-1
50
3
 Price charged (x) 350 450 600 800 1000 Number sold (y) 2500 1450 800 1100 100

Write the equation for line of best fit.

I have tried this about 3 times yet I keep getting the wrong answer. I know the answer is y = -2.96x + 3085.74 but I keep getting answers like y = -10.5x + 26600. What step am I missing or what am I doing wrong? I know I'm missing something but I just don't know what. Please help and maybe show how to get the correct answer because I'm lost. Thank you in advance.

Mar 24, 2020

#1
+111330
+1

Here's  the procedure....hang on....there are a few steps here

Take  the  mean of the  x values  = 640

Take  the  mean of  the y values  = 1190

Calculate  the  difference  between  each x value  and  the  mean of the  x values   and do  the same  for the y values

350 - 640  =     -290               2500 -  1190   =  1310

450  - 640  =   -190                1450  -  1190  =   260

600 - 640   =      -40                  800 -  1190   =  -390

800 -  640   =    160                 1100 - 1190   =   -90

1000 - 640  =    360                 100 - 1190 =   -1090

Take  the products  of these results  and  add them

(-290)(1310) + (-190)(260) +  (-40)(-390)  + (160)(-90) + (360)(-1090)   =  -820500     (1)

Square  each  value  in the  first column above  and add them together   =

(-290)^2  + (-190)^2  + (-40)^2  + (160)^2  + (360)^2   =  277000     (2)

The slope of  the line =  (1) / (2)  =  - 2.96

The  y  intercept  (b) is  found  as

b = average of  y values  -  (slope  * average of  x values)

b  = 1190  - ( [-820500/277000] * 640)    = 3085. 74

So....our line  is

y = -2.96x  + 3085.74

Mar 24, 2020
edited by CPhill  Mar 24, 2020
#2
0

Oh okay, I was using the wrong formula for the slope I think. My teacher gave us the y2-y1/x2-x1 formula to use. Is there a way to get the same answer but using this formula? Thank you for your help. I greatly appreciate it.

Guest Mar 24, 2020
#3
+111330
0

I don't know how to generate  the  slope  using  the "regular" procedure.....

But....apparently.....this method must work just fine.....

CPhill  Mar 24, 2020