The parameter estimates, b 0 = 42.3 and b 1 = 0.49, were obtained using the least squares method. The line passing through the data points is the graph of the estimated regression equation: ŷ = 42.3 + 0.49 x. Values of the independent variable, stress test score, are given on the horizontal axis, and values of the dependent variable, blood pressure, are shown on the vertical axis. The data are shown graphically in the figure, called a scatter diagram. Assume that both a stress test score and a blood pressure reading have been recorded for a sample of 20 patients. The graph of the estimated regression equation for simple linear regression is a straight line approximation to the relationship between y and x.Īs an illustration of regression analysis and the least squares method, suppose a university medical centre is investigating the relationship between stress and blood pressure. Using these estimates, an estimated regression equation is constructed: ŷ = b 0 + b 1 x. For simple linear regression, the least squares estimates of the model parameters β 0 and β 1 are denoted b 0 and b 1. The least squares method is the most widely used procedure for developing estimates of the model parameters. SpaceNext50 Britannica presents SpaceNext50, From the race to the Moon to space stewardship, we explore a wide range of subjects that feed our curiosity about space!Įstimated regression equation, in statistics, an equation constructed to model the relationship between dependent and independent variables.Įither a simple or multiple regression model is initially posed as a hypothesis concerning the relationship among the dependent and independent variables. The least-squares regression line formula is based on the generic slope-intercept linear equation, so it always produces a straight line, even if the data is nonlinear (e.g.
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LINEAR REGRESSION EQUATION EXAMPLE EQUATION HOW TO
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