## How to calculate a line-of-best-fit equation (y=mx+b) from a simple x-y dataset, and then to use this equation to calculate r-square?

### Alan Mason (view profile)

on 16 Jun 2011
Accepted Answer by Sean de Wolski

### Sean de Wolski (view profile)

Hi,

As stated in the title, I am trying to calculate a line-of-best-fit equation (y=mx+b) from a simple x-y dataset, and then to use this equation to calculate r-square.

At the moment I have the following syntax defining the x & y variables:

x1=dat(:,8); y1=dat(:,14);

But I am unsure of where to go from here. I have been searching these forums & MATLAB Help but I have been unable to find a workable solution.

Therefore my 2 questions are: 1. How do I use MATLAB to get a line-of-best-fit equation for this x-y dataset? 2. How do I use this equation (in conjuction with the x-y dataset) to calculate r-square?

Also, I am new to MATLAB so please go easy on me!

Thanks,

Alan

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### Sean de Wolski (view profile)

on 16 Jun 2011
```doc polyfit
```

and then

```doc polyval
doc corrcoef
```

like magic!

Matt Tearle

### Matt Tearle (view profile)

on 16 Jun 2011

that's polyfit (not polytfit)

Sean de Wolski

### Sean de Wolski (view profile)

on 16 Jun 2011

Thanks, my keyboard has it in for me today!

### Matt Tearle (view profile)

on 16 Jun 2011

Approach 1: what Sean said. (Note corrcoef gives the correlation coefficient r, not the coefficient of determination r^2)

Approach 2: use regress, if you have Statistics Toolbox. This allows all sorts of fancy stuff beyond just a fit, as well as post-fit diagnostics.

Approach 3: DIY:

```F = [x1.^0 x1];           % make design matrix [1,x]
c = F\y1                  % get least-squares fit
res = y1 - F*c;           % calculate residuals
r2 = 1 - var(res)/var(y)  % calculate R^2
```

Alan Mason

### Alan Mason (view profile)

on 17 Jun 2011

A actually used this answer - the DIY seemed the most logical choice.

### Alan Mason (view profile)

on 17 Jun 2011

Thank you both for replying. I actually went with Matt's DIY approach (as this showed the logical steps) and it worked great. The rest of my code I'm not so sure about, but that's another story.....

Here's what I ended up with (practically a copy of Matt's DIY code):

%curve fitting model #1 vpd&LE

x1=dat(:,8);

y1=dat(:,14);

% rsquare_vpd

% make design matrix [1,x]

F1 = [x1.^0 x1];

% get least-squares fit

c1 = F1\y1;

% calculate residuals

res1 = y1 - F1*c1;

% calculate R^2

rsquare_vpd = 1 - var(res1)/var(y1);