In regression, “b” refers to the coefficients in the equation that defines the best-fit line through your data. Depending on the notation your textbook or software uses, “b” can represent the slope, the intercept, or both. The most common formula you’ll see is ŷ = a + bx, where b is the slope of the line. In other notation, b₀ is the intercept and b₁ is the slope. Understanding what these numbers tell you is the key to reading any regression output.
The Regression Equation and Where “b” Fits
A simple linear regression draws a straight line through a scatterplot of data points. That line is described by an equation, and there are two main ways you’ll see it written:
- ŷ = a + bx, where “a” is the y-intercept and “b” is the slope
- ŷ = b₀ + b₁x, where b₀ is the y-intercept and b₁ is the slope
Both equations say the same thing. The first version is closer to the y = mx + b formula from algebra class, just with the letters rearranged. The second version, with subscripts, is more common in statistics courses and software output because it scales cleanly when you add more predictor variables (b₂, b₃, and so on).
If your instructor or textbook simply refers to “b” without a subscript, they almost always mean the slope.
What the Slope (b₁) Actually Tells You
The slope is the most important number in a regression equation. It tells you how much the outcome variable changes for every one-unit increase in the predictor variable. If b₁ is 4.854 in a model predicting weight from height, that means each additional inch of height is associated with an increase of about 4.85 pounds in predicted weight.
A positive slope means the two variables move in the same direction: as one goes up, so does the other. A negative slope means they move in opposite directions. For example, a study of skin cancer mortality across U.S. states found a slope of -5.98 for latitude, meaning that for every degree farther north a state sits, the predicted skin cancer mortality rate dropped by about 6 per 100,000.
The size of the slope depends entirely on the units you’re measuring. A slope of 0.02 isn’t necessarily “small” and a slope of 150 isn’t necessarily “large.” What matters is the context: 0.02 miles per dollar spent on gas is a very different story than 0.02 deaths per unit of pollution.
What the Intercept (b₀) Tells You
The intercept is the predicted value of your outcome when the predictor variable equals zero. In the weight-and-height example, b₀ would be the predicted weight of someone who is zero inches tall. That’s obviously meaningless in real life, and this is a common situation. The intercept often exists just to anchor the line mathematically rather than to provide a useful interpretation.
The intercept becomes meaningful when zero is a realistic value for your predictor. If you’re modeling test scores based on hours of studying, the intercept represents the predicted score for someone who didn’t study at all. That’s a number worth paying attention to.
Sample “b” vs. Population “β”
Statistics makes a careful distinction between what you observe in your sample and what’s true for the entire population. The lowercase “b” (b₀, b₁) refers to the values calculated from your specific dataset. The Greek letter beta (β₀, β₁) refers to the true, unknown values in the population that your sample is trying to estimate.
This distinction matters because your sample estimate is never perfect. It’s your best guess at the population value, and it comes with some uncertainty. That uncertainty is where standard errors, confidence intervals, and p-values come in.
How to Tell if “b” Is Statistically Significant
A regression output will give you a b coefficient, but it will also tell you whether that coefficient is meaningfully different from zero. If b₁ isn’t significantly different from zero, it means your predictor may not have a real relationship with the outcome at all. The pattern you see in your sample could just be noise.
Software tests this by dividing the coefficient by its standard error to produce a t-value, then converting that to a p-value. If the p-value is less than 0.05 (the most common threshold), the coefficient is considered statistically significant, meaning you can be reasonably confident it’s not zero in the population. The output will also typically show a 95% confidence interval. If that interval includes zero, the coefficient is not significant at the 0.05 level.
Importantly, a non-significant coefficient doesn’t mean the variable has no effect. It means your data doesn’t provide enough evidence to confirm one. Small sample sizes make it harder to reach significance even when a real relationship exists.
Unstandardized “b” vs. Standardized “β”
When you run a regression with multiple predictors, you might want to compare which predictor has the strongest relationship with the outcome. The problem is that unstandardized b coefficients are tied to each variable’s original units, so comparing them directly is like comparing apples and kilometers.
Standardized coefficients solve this. They’re calculated by multiplying each unstandardized coefficient by the ratio of that predictor’s standard deviation to the outcome’s standard deviation. The result is a number that represents how many standard deviations the outcome changes for every one standard deviation change in the predictor. Because everything is on the same scale, you can directly compare the relative strength of different predictors.
Many research papers report standardized coefficients for exactly this reason. In software output, the unstandardized values are typically labeled “B” or “b,” while standardized values appear as “Beta” or “β.” If you see both columns side by side, the unstandardized column tells you the real-world size of the effect in the original units, and the standardized column tells you which predictors matter most relative to each other. Both are useful for different questions.
Reading “b” in Multiple Regression
Everything above applies to simple regression with one predictor, but the logic extends directly to multiple regression. With several predictors, the equation looks like ŷ = b₀ + b₁x₁ + b₂x₂ + b₃x₃, and each b coefficient tells you how much the outcome changes for a one-unit increase in that predictor, holding all the other predictors constant. That last part is critical. In multiple regression, each coefficient is adjusted for the influence of every other variable in the model, so it isolates the unique contribution of that predictor.
This means a variable’s b coefficient can change dramatically depending on what other variables are in the model. A predictor that looks important on its own might shrink to near zero once you account for a closely related variable. Checking significance for each coefficient helps you identify which predictors are genuinely contributing to the model and which are redundant.