# Simple Linear Regression

09-07-2017 06:17 AM - last edited 04-12-2018 23:19 PM

# Simple Linear Regression

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09-07-2017 06:17 AM - edited 04-12-2018 11:19 PM

This measure allows you to predict dependent values Y from independent values X.

#### NAME:

Simple linear regression

#### DESCRIPTION:

Estimate Y values based on X values.

#### PARAMETERS:

Name: Category

Tooltip: The category for which you have known X and Y values

Type: Categorical field

Name: Measure X

Tooltip: Known X (independent) values

Type: Numerical field / measure

Name: Measure Y

Tooltip: Known Y (dependent) values

Type: Numerical field / measure

#### DAX:

```
Estimated {Measure Y} =
VAR Known =
FILTER (
SELECTCOLUMNS (
ALLSELECTED ( {Category} ),
"Known[X]", CALCULATE ( {Measure X} ),
"Known[Y]", CALCULATE ( {Measure Y} )
),
AND (
NOT ( ISBLANK ( Known[X] ) ),
NOT ( ISBLANK ( Known[Y] ) )
)
)
VAR Count_Items =
COUNTROWS ( Known )
VAR Sum_X =
SUMX ( Known, Known[X] )
VAR Sum_X2 =
SUMX ( Known, Known[X] ^ 2 )
VAR Sum_Y =
SUMX ( Known, Known[Y] )
VAR Sum_XY =
SUMX ( Known, Known[X] * Known[Y] )
VAR Average_X =
AVERAGEX ( Known, Known[X] )
VAR Average_Y =
AVERAGEX ( Known, Known[Y] )
VAR Slope =
DIVIDE (
Count_Items * Sum_XY - Sum_X * Sum_Y,
Count_Items * Sum_X2 - Sum_X ^ 2
)
VAR Intercept =
Average_Y - Slope * Average_X
RETURN
Intercept + Slope * {Measure X}
```

For more details on and other uses of this quick measure, see my blog post on the subject:

https://xxlbi.com/blog/simple-linear-regression-in-dax/

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## Re: Simple Linear Regression

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11-27-2017 05:16 AM

Hi

I am using your Simple Linear Regression measure with great success. Thank You.

I am doing temperature studies and I want to find the first and last values of your measure in a given time interval which is filtered by a slicer. By doing this I can calculate the difference in the trend line over the interval of filtered years.

I can find the first and last **year** of the filtered interval by using FIRSTNONBLANK and LASTNONBLANK but I can't do this with your code because FIRSTNONBLANK and LASTNONBLANK only accept a column as an argument. I cannot seem to convert your measure into a calculated column to do this. Is there a version of your measure that produces a column? My data has two columns **year** and **temperature. **X and Y.

Any help would be much appreciated.

Tony Maclaren

## Re: Simple Linear Regression

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11-28-2017 12:30 AM - edited 11-28-2017 12:59 AM

Thanks for your feedback, Tony!

If I understand you correctly, there are a few ways to achieve your goal.

Here is an example of a measure:

Starting Temperature = VAR Known = FILTER ( SELECTCOLUMNS ( ALLSELECTED ( 'Table'[Year] ), "Known[X]", 'Table'[Year] ), "Known[Y]", [Temperature] ), AND ( NOT ( ISBLANK ( Known[X] ) ), NOT ( ISBLANK ( Known[Y] ) ) ) ) VAR First = TOPN ( 1, Known, Known[X], ASC ) RETURN MINX ( First, Known[Y] )

## Re: Simple Linear Regression

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11-28-2017 11:35 AM

Dear Daniil

Thank you for your very prompt response. I will be in Sydney, where I grew up, in early December!

Here is the tweaked code below (minus some brackets) that does the trick.Thank you so much.

This is an** incredibly useful** companion measure to your Simple Linear Regression measure, and because it works with measures it will find the equivalent of FIRSTNONBLANK in **a measure**. However it does not work correctly in the filtered context of a YEAR slider to filter the interval of years which the Simple Linear Regression measure does .The value changes with the slider, but the results do not correctly match the estimated starting value of the **Estimated** measure except for the first value of the whole dataset.

Starting Temperature =

VAR Known =

FILTER (

SELECTCOLUMNS (

ALLSELECTED ( 'cetdata'[YEAR] ),

"Known[X]", 'cetdata'[YEAR],

"Known[Y]", [Estimated]

),

AND (

NOT ( ISBLANK ( Known[X] ) ),

NOT ( ISBLANK ( Known[Y] ) )

)

)

VAR First =

TOPN ( 1, Known, Known[X], ASC )

RETURN

MINX ( First, Known[Y] )

NOT ( ISBLANK ( Known[Y] ) )

)

)

VAR First =

TOPN ( 1, Known, Known[X], ASC )

RETURN

MINX ( First, Known[Y] )

Now we have to fix the filter context and figure out how to find [**Ending temperature**] so we can subtract **[Starting Temperature]** and get the trend change per filtered interval.

Thanks again--great stuff. No one else had a clue what my problem was or how to solve it.

Tony

## Re: Simple Linear Regression

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11-28-2017 07:24 PM

Tony, you should visit the local Power BI User Group if you get a chance :-) The next meeting date should be announced at Meetup soon.

Try the following measures:

Starting Temperature = VAR Estimate = SELECTCOLUMNS ( KEEPFILTERS ( ALLSELECTED ( 'cetdata'[YEAR] ) ), "Estimate[X]", 'cetdata'[YEAR], "Estimate[Y]", [Estimated] ) VAR First = TOPN ( 1, Estimate, Estimate[X], ASC ) RETURN MINX ( First, Estimate[Y] )

Ending Temperature = VAR Estimate = SELECTCOLUMNS ( KEEPFILTERS ( ALLSELECTED ( 'cetdata'[YEAR] ) ), "Estimate[X]", 'cetdata'[YEAR], "Estimate[Y]", [Estimated] ) VAR Last = TOPN ( 1, Estimate, Estimate[X], DESC ) RETURN MAXX ( Last, Estimate[Y] )

Temperature Difference = [Ending Temperature] - [Starting Temperature]

## Re: Simple Linear Regression

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11-29-2017 05:43 AM

Dear Daniil

Thank you very much--all working perfectly now. KEEPFILTERS did the trick.I have really learned a lot! I have now ordered the SQLBI book.

One strange thing however,The [Estimated] measure which is your Simple linear Regression measure produces a total if displayed in a table. I do not quite understand this.

Best Regards

and thanks again

Tony

## Re: Simple Linear Regression

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12-01-2017 04:45 AM

Really excellent stuff !!

I had managed to do a linear regression line previously but this is so much cleaner

I did have to tweak yours slightly

1) Instead of a plain old Allselected i needed to

do

CALCULATETABLE (

SUMMARIZE (

FeederHistory,

FeederHistory[EventDateHour],

FeederHistory[EventDate]

),

ALLSELECTED ( FeederHistory )

),

and for some reason SSRS moaned at me for using SELCTEDVALUE so I replaced it with the older hasonevalue values paradigm

ie

RETURN

Intercept

+ Slope

* IF (

HASONEVALUE ( FeederHistory[EventDate] ),

VALUES ( FeederHistory[EventDate] ))

## Re: Simple Linear Regression

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12-01-2017 04:48 AM

Really excellent stuff !!

I had managed to do a linear regression line previously but this is so much cleaner

I did have to tweak yours slightly

1) Instead of a plain old Allselected i needed to

do

CALCULATETABLE (

SUMMARIZE (

FeederHistory,

FeederHistory[EventDateHour],

FeederHistory[EventDate]

),

ALLSELECTED ( FeederHistory )

),

and for some reason SSRS moaned at me for using SELCTEDVALUE so I replaced it with the older hasonevalue values paradigm

ie

RETURN

Intercept

+ Slope

* IF (

HASONEVALUE ( FeederHistory[EventDate] ),

VALUES ( FeederHistory[EventDate] ))

## Re: Simple Linear Regression

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12-01-2017 04:51 AM

I know this is a Power Bi portal but I had to make it work for both PBI and SSRS

## Re: Simple Linear Regression

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12-01-2017 09:04 AM

Hi

Thanks for your comments. If, like me you ever need to get the first and last values for a given filtered interval to calculate the total trend change over time, or rate of trend change over time, the Starting and Ending measures are great. When you get something like this working it really puts a smile on your face! With these complicated measures I can highly recomment DAX formatter if you are not already using it.

Tony