Graphing Base Form of y=mx+b from a .csv file

I have a few thousand equations in y=mx+b form that I have acquired from hundreds of thousands of data points in multiple excel files. They are all trendlines of similar T-s data. I am attempting to create generalized trendlines of similar data types and I would like to be able to select formulas in y=mx+b form that I would like plotted, and then find the formula for the LOBF (Line of best fit) for that set of equations. I am new to MatLab and would just like some assistance in this.

[Adam Danz]

"I have a few thousand equations in y=mx+b form"

Does that mean you have a few thousand slope (m) and intercept (b) values? Or do you have a few thousand strings or character arrays where m and b contain numbers (like, 'y = 0.5x + 1')?

[Nathan Rivard]

The latter. I have strings in the form of y-mx+b as you showed above.

[Adam Danz]

We're still doing a lot of guessing here. How are your data stored? In a cell array of characters like this?

eq = {'y=.5x+1'
      'y=.3x+3'
      'y=.2x+4'
      'y= 1x+5'
      'y=.9x+3'
      .
      .
      .
      .       }

[Nathan Rivard]

In a .csv in the format of

10G,y = 2.3297x + 107.25,y = 1.8866x + 104.63,y = 0.3373x + 104.19,y = 3.584x + 69.269,y = 2.1044x + 66.54,y = 0.0704x + 68.264,,,
15G,y = 1.9526x + 96.634,y = 1.7754x + 92.007,y = 2.774x + 68.856,y = 3.0042x + 62.398,y = 2.3015x + 59.709,y = 0.1415x + 63.591,,,
20G,y = 1.9004x + 95.721,y = 1.9833x + 88.81,y = 3.1304x + 65.163,y = 3.1099x + 63.696,y = 2.466x + 60.485,y = 0.2486x + 62.237,,,

[Adam Danz]

Have you read the data into matlab already?

If yes, how do the data appear in matlab?

If no, we'll have to figure that out first. Are the lines above single rows? Maybe attaching the file would help if you haven't read in the data yet.

Lots of missing information, still.

[Nathan Rivard]

The data appears in cell format, similar to excel with the lines corresponding to the array. First cell is in (1,1) and so on for about 8 cells. They are in seperate cells

[Adam Danz]

I don't have enough information to suggest how to read in the data. You could use Matlab's Import Data tool to start with. To use my solution below, you'll need to import the file as a cell array of strings or character arrays. You'll also need to get rid of the first column of numeric data since my answer expects that all elements of the cell array are strings.

If you get stuck, let me know where you're at.

[Nathan Rivard]

The data was already imported through the import data tool and is sitting in a table of variables in MatLab. I got rid of the first column of numeric data as well but I will continue work onto tomorrow and post an update. Thank you for the help

[Adam Danz]

That info is helpful. If you're reading it in as a table and you already got rid of the first column, the first line of my solution will be

numVals = regexp(data{:,:},'[+-]?\d+\.?\d*', 'match');
%                    ^^^^^ add this

Alternatively, if you hadn't removed the first column, you could have done,

numVals = regexp(data{:,2:end},'[+-]?\d+\.?\d*', 'match');
%                    ^^^^^^^^^

The rest of my solution will be the same.

Answer 1

[Adam Danz]

I'm assuming you've read the data into Matlab and you've got a cell array of strings or character arrays named "data" that appears like this:

data =
  3×6 cell array
  Columns 1 through 3
    {'y = 2.3297x + 1…'}    {'y = 1.8866x + 1…'}    {'y = 0.3373x + 1…'}
    {'y = 1.9526x + 9…'}    {'y = 1.7754x + 9…'}    {'y = 2.774x + 68…'}
    {'y = 1.9004x + 9…'}    {'y = 1.9833x + 8…'}    {'y = 3.1304x + 6…'}
  Columns 4 through 6
    {'y = 3.584x + 69…'}    {'y = 2.1044x + 6…'}    {'y = 0.0704x + 6…'}
    {'y = 3.0042x + 6…'}    {'y = 2.3015x + 5…'}    {'y = 0.1415x + 6…'}
    {'y = 3.1099x + 6…'}    {'y = 2.466x + 60…'}    {'y = 0.2486x + 6…'}

Execute these two lines below to extract the slope and intercept values from each string.

numVals = regexp(data,'[+-]?\d+\.?\d*', 'match');
mb = cellfun(@str2double, numVals, 'UniformOutput', false); 

mb is a cell array the same size as "data" and contains the [slope,intercept] of each cell element.

mb =
  3×6 cell array
    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}
    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}
    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}    {1×2 double}

For example, for the equation in data(2,3), the slope and intercept are

   mb{2,3}
ans =
        2.774       68.856

To draw a regression line on a plot use refline()

 refline(mb{2,3})

[Nathan Rivard]

This is the error I get when attempting to do this. I create an 8x1 table of the data that I would like to create a single regression line from, but when I input that data as the name 'data' I get this error when creating mb

>> data = Gal50KBTUEquationComparison

data =

  8×1 table

             KBTU         
    ______________________

    "y = 1.9744x + 100.29"
    "y = 2.1726x + 96.719"
    "y = 2.1106x + 96.177"
    "y = 1.8326x + 96.032"
    "y = 1.7545x + 95.098"
    "y = 1.8422x + 87.252"
    "y = 1.9528x + 84.051"
    "y = 2.1788x + 74.386"

>> numVals = regexp(data,'[+-]?\d+\.?\d*', 'match');
mb = cellfun(@str2double, numVals, 'UniformOutput', false); 
Error using regexp
The 'STRING' input must be either a char row vector, a cell array of char row vectors, or a string array.

[Adam Danz]

That's because "data" in my answer is a cell array. "data" in your example is a table. To extract the values in your table so that they are in the form of a cell array, try

numVals = regexp(data{:,:},'[+-]?\d+\.?\d*', 'match');
%                    ^^^^^

as explained earlier, here.

[Nathan Rivard]

Ok, I would once again like to thank you so much for your help thus far. I have been able to create the regression line of a single equation. Now, I would like to create a single regression line of the set of 8 equations I have listed above and print out the string of the equation as well

[Adam Danz]

Glad I can help!

There is no single regression line for 8 difference slopes and intercepts.

Do you mean you want to average the slopes and average the intercepts? Maybe compute the medians? Note that if you've got both positive and negative slopes, the mean slope could be a poor representation of the distribution of slopes.

[Nathan Rivard]

Ok one more thing and I will 100% accept it. I would like the average of the slopes and the average of the intercepts seperately as none of the slopes are negative and they are all remotely close together

[Adam Danz]

Continuing from the mb cell array in my answer,

allSlopes = cellfun(@(x)x(1),mb); %matrix of all slopes in mb
allInt = cellfun(@(x)x(2),mb);    %matrix of all intercepts in mb
 
meanSlope = mean(allSlopes(:)); 
meanYint = mean(allInt(:));