Question

How do you change a linear function based on changes in the real world?

Answer 1

can you be more specific?

Answer 2

im not exactly sure how to be more specific. Sorry

Answer 3

you mean, you have real life data and want to ajust a linear function that best fits this data?

Answer 4

i believe so

Answer 5

there are some method to do this, there is Linear Regression, Least Square Fitting

Answer 6

ok. may you explain what those are please

Answer 7

you want to ajust a line in the form \(y = ax + b\) using the set of data \( (x_i, y_i) \) where \( i = 0, 1,2,...,N \). \(N\) is the amount of real life data you have

Answer 8

So what we need to do is find \(a\) and \(b\)

Answer 9

My favorite method is linear regression

Answer 10

From calculus, you can find that:
\[\large a = \frac{\sum_{i=0}^{N} x_iy_i \space -\frac{1}{N}\sum_{i=0}^{N} x_i \sum_{i=0}^{N} y_i}{\sum_{i=0}^{N} x_i^2 \space -(\sum_{i=0}^{N} x_i)^2} \]

Answer 11

From calculus, you can find that:
\[\large b = \frac{1}{N}\sum_{i=0}^{N}y_i \space -a\frac{1}{N}\sum_{i=0}^{N}x_i\]

Answer 12

if you want to know more about the process involved, go to http://mathworld.wolfram.com/LeastSquaresFitting.html

Answer 13

and here http://en.wikipedia.org/wiki/Simple_linear_regression