Question

Using the data below, what is the equation for the line of best fit? Remember, put your answer in y = ax + b form and round any decimals to three places.
Patient Calories Wt. loss/week lbs.
1 1500 2
2 1200 3
3 1800 1
4 2100 .5
5 2400 .75
6 1800 1
7 1200 5
8 2100 1
9 2400 .5
10 1500 2

Answer 1

You can use many methods in curve fitting, a good one for linear fitting is the Linear least squares

Answer 2

how do you do that???

Answer 3

As you need a linear fitting, you must solve a 2x2 linear system:
Ax=B
Where\[A = \left[\begin{matrix}n & \sum_{i=1}^{n}x_i \\ \sum_{i=1}^{n}x_i & \sum_{i=i}^{n}{x_i}^{2}\end{matrix}\right]\]

\[x = \left(\begin{matrix}a \\ b\end{matrix}\right)\]

\[B=\left(\begin{matrix}\sum_{i=1}^{n}y_i \\ \sum_{i=1}^{n}x_iy_i\end{matrix}\right)\]

Whre n is the number of data in your table

Answer 4

solving this system you will find the values for a and b so that the data your tables best fits in a linear curve y = ax+b

Answer 5

y = -266.574x + 2246.512 ; this is what I keep getting, but it doesn't look right

Answer 6

there are 2 possibilities, patient x Calories or patient x Wt. loss/week lbs.

Answer 7

which one you need?

Answer 8

I think patient x calories

Answer 9

sorry i wrote wrong, after you solve the linear system, you will find a and b such that y= a+bx best fits you data

Answer 10

i found y = 1559.603 + 43.709x

Answer 11

use x = [1,2,3,4,5,6,7,8,9,10] and y = [1500,1200,1800,2100,2400,1800,1200,2100,2400,1500]