# Interpreting the slope and intercept in a linear regression model

## Interpret the slope and intercept of a regression line

Interpreting the slope and intercept in a linear regression model. Example 1. Data were collected on the depth of a dive of penguins and the duration of the dive.

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Now we focus on the equation of a line in more detail. Our goal is to understand what the numbers in the equation tell us about the relationship between the explanatory variable and the response variable. Here are some of the equations of lines that we have used in our discussion of linear relationships:. When we find the least-squares regression line, a and b are determined by the data. The values of a and b do not change, so we refer to them as constants. It is called initial value.

This tutorial is going to cover interpretation of what the slope and y-intercept of a least-squares regression line actually mean. So let's take a look. A slope is a rate of change. Now, you've talked about rates of change a lot in everyday life. The examples of common rates that you might use in everyday life are miles per hour. That's how many miles you'll travel if you increase your time in the car by one hour.

If X never equals 0, then the intercept has no intrinsic meaning. In scientific research, the purpose of a regression model is to understand the relationship between predictors and the response. You do need it to calculate predicted values, though. In market research, there is usually more interest in prediction, so the intercept is more important here. When X never equals 0 is one reason for centering X. Dummy coded variables have values of 0 for the reference group and 1 for the comparison group. This is especially important to consider when the dummy coded predictor is included in an interaction term.

The slope indicates the steepness of a line and the intercept indicates the location where it intersects an axis. The slope and the intercept define the linear relationship between two variables, and can be used to estimate an average rate of change. The greater the magnitude of the slope, the steeper the line and the greater the rate of change.
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By Deborah J. In statistics, once you have calculated the slope and y- intercept to form the best-fitting regression line in a scatterplot, you can then interpret their values. The slope is interpreted in algebra as rise over run. In a regression context, the slope is the heart and soul of the equation because it tells you how much you can expect Y to change as X increases. In general, the units for slope are the units of the Y variable per units of the X variable. Suppose in studying the effect of dosage level in milligrams mg on systolic blood pressure mmHg , a researcher finds that the slope of the regression line is —2.

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## Slope and intercept of the regression line

Regression: Slope, intercept, and interpretation

## Interpreting the Intercept in a Regression Model

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1. Juliano S. says:

Interpreting slope and y-intercept for linear models (practice) | Khan Academy

2. Shannon L. says:

Interpreting slope and y-intercept for linear models. AP Stats: Joyce created the following scatterplot and regression line to show this relationship. The fitted.

3. Eve D. says: