Contributor
Posts: 20

# Expressing logistic and linear regression output into an equation

I need to express my linear regression model as an equation so that I can calculate the predictions separately (ie, outside SAS). Ditto for my logistic regression model. Could you confirm whether I'm doing this correctly?

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LINEAR regression parameter estimates (using proc genmod)

• Intercept: 3.9273
• var1: 0.0015

I've expressed the equation as:     prediction   =   3.9273 + 0.0015*var1

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LOGISTIC regression parameter estimates (using proc logistic, binary, solving for "1")

• Intercept: -2.8240
• var2: 1.2638

I've expressed the equation as:    probability   =   exp(-2.8240 + 1.2638*var2)   /   (1 + exp(-2.8240 + 1.2638*var2))

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Yes, no, maybe so??? I need to confirm because when I do this, the answers do not match what I get when scoring in SAS directly. Thank you!

Super User
Posts: 20,785

## Re: Expressing logistic and linear regression output into an equation

Here's a good thread on this topic.

https://communities.sas.com/t5/SAS-Statistical-Procedures/How-to-determine-logistic-regression-formu...

It has a worked example, the Neuralgia dataset is in SAS documentation if you want to test the code.

Also, look at the CODE statement in those procs if you're in SAS/STAT 13+

This will generate sas data step code that will score your data.

Or you can use PROC SCORE or the SCORE statement within those procs.

SAS Employee
Posts: 310

See this note.

Contributor
Posts: 20

## Re: Expressing logistic and linear regression output into an equation

Not finding the answer yet. Sorry for being a numbskull. I'll try to be more specific.

PART 1: My linear regression code:

```proc genmod data = mydataset;
model amount = var1 / link = log
dist = gamma
type3;
output out = myoutput
p = pred;
run;```

The resulting parameter estimates:

• Intercept: 3.9273
• var1: 0.0015

This is a gamma distribution with a log link, so I guess that complicates matters. How should I translate this into an actual mathematical equation?

PART 2: My logistic regression code:

```proc logistic data = my_training_dataset
outmodel = my_model_info;
model responded (event = '1') = var2 /selection = stepwise
lackfit
rsq;
run;

proc logistic inmodel = my_model_info;
score data = my_dataset_to_score
out  = my_scored_dataset;
run;```

The resulting parameter estimates:

• Intercept: -2.8240
• var2: 1.2638

How should I translate this into an actual mathematical equation?

Super User
Posts: 20,785

## Re: Expressing logistic and linear regression output into an equation

Use the CODE statement in either proc and examine the output.

The initial thread I linked too walked through the solution for LOGISTIC regression in detail so I'm not sure what I could add besides replicating it specifically for your exact values.

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