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- Calculating linear regression slope in formula

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Feb 27, 2017 10:52 AM
(4950 views)

Hello,

I was wondering if there was a way to calculate the linear regression slope of column data within a data table formula.

A simple example of the table is below. The data is ordered and I would like to calculate the slope of a fit line of volume over time using the current row's data and previous points to perform the regression.

The idea is that I would like to see the how the calculated slope changes with increasing the number of data points. From doing this manually, the slope values end up approaching a given value and stay within +/-5% after 20 or so points.

Instance | Time (s) | Volume (mL) | Slope (mL/s) |

1 | 0 | 0 | n/a |

2 | 5 | 0.5 | m1 |

3 | 10 | 0.8 | m2 |

... | ... | ... | ... |

N | T | V | mN-1 |

If that is possible, my next challenge would be to set this up so that I can calculate the slope formula so that it uses N data points on either side of the current row for a symmetrical moving calculation instead.

Thank you in advance.

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Feb 27, 2017 12:53 PM
(9287 views)

You could also use a column formula. I opened Big Class.jmp from the Sample Data folder. (Select **Help** > **Sample Data Library** > **Big Class.jmp** > **Open**) I crated a new numeric column called **moving slope**. This example computes the moving slope with a span of 3 for Y = weight and X = height with the following column formula:

```
If( Row() > 1,
x = J( Row(), 1, 1 ) || :height[Index( 1, Row() )]`;
y = :weight[Index( 1, Row() )]`;
(Inv( x` * x ) * x` * y)[2];
,
Empty()
)
```

Then plot moving slope versus row in Graph Builder.

Learn it once, use it forever!

10 REPLIES

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Feb 27, 2017 12:15 PM
(4873 views)

Here is a script that gives you the output you want, it just does it a different way. It uses the Fit Model Platform and loops through it several time, increasing the N.

```
Names Default To Here( 1 );
dt = Open( "$SAMPLE_DATA\semiconductor capability.jmp" );
// Create an output table to hold the results
dtOut = New Table( "summary",
New Column( "Instance" ),
New Column( "N" ),
New Column( "RSquare" ),
New Column( "RSM" ),
New Column( "Intercept" ),
New Column( "b1" ),
New Column( "b2" )
);
Loop Counter = 0;
// Loop across the different sizes
For( i = 5, i <= 111, i = i + 5,
Loop Counter++;
// Create a random sample data table from the original data table
dt << New Column( "random", formula( Random Uniform() ) );
dt << sort( by( dt:random ), , Order( Ascending ), replace table( 1 ) );
dt << delete columns( "Random" );
dt << select where( Row() <= i );
dtSample = dt << subset( invisible, selected rows( 1 ), selected columns( 0 ) );
// Run the regression
fm = dtSample << Fit Model(
Y( :NPN1 ),
Effects( :PNP1, :PNP2 ),
Personality( "Standard Least Squares" ),
Emphasis( "Minimal Report" ),
Run(
:NPN1 << {Summary of Fit( 1 ), Analysis of Variance( 1 ), Parameter Estimates( 1 ),
Lack of Fit( 0 ), Plot Actual by Predicted( 0 ), Plot Regression( 0 ),
Plot Residual by Predicted( 0 ), Plot Effect Leverage( 0 )}
)
);
// Capture the output data
dtOut << Add Rows( 1 );
dtOut:Instance[N Rows( dtOut )] = Loop Counter;
dtOut:N[N Rows( dtOut )] = i;
dtOut:RSquare[N Rows( dtOut )] = (Report( fm )["Summary of Fit"][1][2] << get)[1];
dtOut:RSM[N Rows( dtOut )] = (Report( fm )["Summary of Fit"][1][2] << get)[3];
dtOut:Intercept[N Rows( dtOut )] = (Report( fm )["Parameter Estimates"][1][3] << get)[1];
dtOut:b1[N Rows( dtOut )] = (Report( fm )["Parameter Estimates"][1][3] << get)[2];
dtOut:b2[N Rows( dtOut )] = (Report( fm )["Parameter Estimates"][1][3] << get)[3];
// Clean up after our selfs
fm << close window;
Close( dtSample, nosave );
);
```

Jim

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Feb 27, 2017 12:52 PM
(4858 views)

Try plugging this formula into a new formula column (this will calculate the slope up to the current row):

(Row() * Summation( i = 1, Row(), :Time[i] * :Volume[i] )

-Summation( i = 1, Row(), :Time[i] ) * Summation( i = 1, Row(), :Volume[i] )) / (

Row() * Summation( i = 1, Row(), :Time[i] ^ 2 )

-Summation( i = 1, Row(), :Time[i] ) ^ 2)

To do the second part of your question would only require changing the index on the summation, i.e. from i=Row()-N to Row()+N.

Hope this helps.

-Jerry

(Row() * Summation( i = 1, Row(), :Time[i] * :Volume[i] )

-Summation( i = 1, Row(), :Time[i] ) * Summation( i = 1, Row(), :Volume[i] )) / (

Row() * Summation( i = 1, Row(), :Time[i] ^ 2 )

-Summation( i = 1, Row(), :Time[i] ) ^ 2)

To do the second part of your question would only require changing the index on the summation, i.e. from i=Row()-N to Row()+N.

Hope this helps.

-Jerry

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Feb 27, 2017 12:53 PM
(9288 views)

You could also use a column formula. I opened Big Class.jmp from the Sample Data folder. (Select **Help** > **Sample Data Library** > **Big Class.jmp** > **Open**) I crated a new numeric column called **moving slope**. This example computes the moving slope with a span of 3 for Y = weight and X = height with the following column formula:

```
If( Row() > 1,
x = J( Row(), 1, 1 ) || :height[Index( 1, Row() )]`;
y = :weight[Index( 1, Row() )]`;
(Inv( x` * x ) * x` * y)[2];
,
Empty()
)
```

Then plot moving slope versus row in Graph Builder.

Learn it once, use it forever!

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Feb 27, 2017 9:17 PM
(4841 views)

This is exactly what I was looking for. I had no idea these operations were available!

Thank you!

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Jul 26, 2017 9:52 PM
(3700 views)

wow~~ Awesome!!!!!!

Thank you so much!!!!! : )

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Jan 23, 2018 8:07 AM
(1657 views)

Hi

I am trying to apply your formula to calculate the moving slope with a window of 8, by which I mean (for Row() > 7), I want to calculate the slope of the linear regression for the first set of x and y data points [1 to 8], and then the next set of 8 data points incrementing by 1 [2 to 9], and so on. I am trying to calculate the maximum slope to get the initial rate of an enzymatic reaction.

Please can you tell me how you would modify your script to achieve this? I have tested your formula and I obtain the slope for all data points from Row 1 to Row n, rather than a moving window of defined size.

Thank you in advance

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Jan 23, 2018 8:27 AM
(1653 views)

This modified formula produces a moving slope of span 8:

```
If( Row() > 7,
x = J( 8, 1, 1 ) || :height[Index( Row() - 7, Row() )]`;
y = :weight[Index( Row() - 7, Row() )]`;
(Inv( x` * x ) * x` * y)[2];
)
```

Learn it once, use it forever!

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Jan 23, 2018 8:43 AM
(1643 views)

Excellent, that works, thank you

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Sep 10, 2018 11:36 AM
(375 views)

Hi,

Is there any plan to put slope and intercept into formula builder of a future JMP version w/ a more straight forward direct function ?

thx.