What the Heck is Beta?
A simple linear regression example with %AI Adoption & Employee Counts
Believe it or not, the question about “what is Beta” comes up in various forms when I work with clients. And many years ago, it was this question that made me realize why communication is hard when technical jargon meets the real world.
Beta is typically the slope of a regression analysis in the world of data science and statistics. It represents the change in the variable of interest CAUSED by a unit change in another variable.
Still confusing, right? That's where I hope my example today helps. I made up these numbers to keep things simple.
Example to Understand Beta
Consider 30 SMBs as our sample.
They have anywhere from 2 to 20 employees each (X).
We are interested in studying %AI adoption rates (Y).
Estimate relationship with number of employees.
Y = a + bX (simple linear regression model) is used.
Estimating the model for the data yields:
Y = 68 - 0.6X
Here, the (-0.6) is the BETA or the slope. It shows the average impact of an extra employee on the AI Adoption Rate of a given SMB. For every additional employee, AI adoption rate decreases by 0.6%.
This is the AVERAGE impact. There could be SMBs with a higher or lower impact. So, note that the beta shows the EXPECTED impact.
Now, one can ask... can this be extrapolated to the full population of all SMBs? The answer is "Yes, but with extreme caution."
Here's why
The confidence interval of Beta is (-0.74, -0.49).
95% of SMBs AI adoption rate drops between 1/2 to 3/4%.
Our sample SMBs only had 2-20 employees.
Our sample size was pretty small at about 30 SMBs
We should not generalize this result about all other SMBs.
Actionable Insights
Use Beta values to measure only what applies to sample.
When making decisions, recognize the data limitations.
Repeated estimates over time yield better results.
AI tools and statistical software can calculate.
Interpretation of results requires expertise.
Always seek clarification on statistics.
Have a data-translator help you.
P.S.: What is ONE question regarding statistics that I can answer for you?
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