estimated simple linear regression equation

For a given value of X, we can estimate the average value of Y and write this as a conditional expectation E( Y| X), often written simply as μ( X). In simple regression, there is one independent variable, X, and one dependent variable, Y. We say there is a regression relationship between X and Y when the mean of Y varies with X. The predictor variable may also be randomly selected, but we treat it as fixed when making predictions (for example, predicted weight for someone of a given height). Typically, in correlation we sample both variables randomly from a population (for example, height and weight), and in regression we fix the value of the independent variable (for example, dose) and observe the response. One of the simplest prediction methods is linear regression, in which we attempt to find a 'best line' through the data points.Ĭorrelation and linear regression are closely linked-they both quantify trends. If we suspect a trend, we may want to attempt to predict the values of one variable using the values of the other.

We discussed correlation as a type of association in which larger values of Y are associated with larger values of X (increasing trend) or smaller values of X (decreasing trend) 2. We have previously defined association between X and Y as meaning that the distribution of Y varies with X.

Estimated simple linear regression equation