#THE SIMPLE LINEAR REGRESSION EQUATION HOW TO#

In contrast, the graph below depicts the relationship between BMI and HDL cholesterol in the same sample of n=20 participants. In contrast, suppose we examine the association between BMI and HDL cholesterol. The graph shows that there is a positive or direct association between BMI and total cholesterol participants with lower BMI are more likely to have lower total cholesterol levels and participants with higher BMI are more likely to have higher total cholesterol levels. Note that the independent variable (BMI) is on the horizontal axis and the dependent variable (Total Serum Cholesterol) on the vertical axis. Each point represents the observed (x, y) pair, in this case, BMI and the corresponding total cholesterol measured in each participant. The figure below is a scatter diagram illustrating the relationship between BMI and total cholesterol. (If a different relationship is hypothesized, such as a curvilinear or exponential relationship, alternative regression analyses are performed.) This analysis assumes that there is a linear association between the two variables. When there is a single continuous dependent variable and a single independent variable, the analysis is called a simple linear regression analysis. So, in this case, Y=total cholesterol and X=BMI. In regression analysis, the dependent variable is denoted Y and the independent variable is denoted X. For example, suppose we want to assess the association between total cholesterol (in milligrams per deciliter, mg/dL) and body mass index (BMI, measured as the ratio of weight in kilograms to height in meters 2) where total cholesterol is the dependent variable, and BMI is the independent variable. Simple linear regression is a technique that is appropriate to understand the association between one independent (or predictor) variable and one continuous dependent (or outcome) variable. We introduce the technique here and expand on its uses in subsequent modules. This equation matches the one that we calculated by hand.Regression analysis is a widely used technique which is useful for many applications. We can double check our results by inputting our data into the simple linear regression calculator: A one pound increase in weight is associated with a 0.2001 inch increase in height. When weight is zero pounds, the predicted height is 32.783 inches. Sometimes the value for b 0 can be useful to know, but in this example it doesn’t actually make sense to interpret b 0 since a person can’t weigh zero pounds.ī 1 = 0.2001.

#THE SIMPLE LINEAR REGRESSION EQUATION HOW TO#

Here is how to interpret this estimated linear regression equation: ŷ = 32.783 + 0.2001xī 0 = 32.7830. In our example, it is ŷ = 0.32783 + (0.2001)*x How to Interpret a Simple Linear Regression Equation

The estimated linear regression equation is: ŷ = b 0 + b 1*x Step 5: Place b 0 and b 1 in the estimated linear regression equation. Use the following steps to fit a linear regression model to this dataset, using weight as the predictor variable and height as the response variable. Suppose we have the following dataset that shows the weight and height of seven individuals: Example: Simple Linear Regression by Hand

This tutorial explains how to perform simple linear regression by hand. Simple linear regression is a statistical method you can use to quantify the relationship between a predictor variable and a response variable.

The simple linear regression equation