It is also possible to evaluate the properties under other assumptions. Where, a0 It is the intercept of the Regression line (can be obtained putting x0) a1 It is the slope of the regression line, which tells whether the line is increasing or decreasing. This is based on the assumption of the validity of a model under which the estimates are optimal. The Simple Linear Regression model can be represented using the below equation: y a 0 +a 1 x+. The description of statistical properties of estimators, from a simple linear regression, estimates require a statistical model. Participants’ predicted weight is equal to -234.58 +5.43 (Height) pounds when height is measured in inches. A significant regression equation was found (F (1,14) 25.926, p <. The linear combination of the residuals, in which the coefficients are the x-value, is equal to zero A simple linear regression was calculated to predict participant’s weight based on their height.Assumptions of linear regression If youre thinking simple linear regression may be appropriate for your project, first make sure it meets. The sum of the residuals is equal to zero, if the model includes a constant The formula for simple linear regression is Y mX + b, where Y is the response (dependent) variable, X is the predictor (independent) variable, m is the estimated slope, and b is the estimated intercept.The line goes through the “center of mass” points (x(bar), y(bar)).There are three numerical properties of simple linear regression. The intercept of the fitted line is such that it passes through the center of mass of the data points. The slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. “Simple” refers to the fact that this regression is one of the simplest in statistics. Simple linear regression fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model as small as possible. Simple linear regression is the least squares estimator of a linear regression model with a single explanatory variable.