Typically, an analyst will not have to calculate regression coefficients by hand. To determine the slope and intercept of the regression line, one must either use a statistical calculator, a software program, or calculate it by hand. Linear regression involves finding a straight line that fits the scatter plot best. The process of determining these parameters involves calculus. The process of linear regression calculates the parameters as those that minimize the squared deviations of the actual data values from the estimated values obtained using the regression equation. The slope, of course, represents the ratio of the vertical rise in the line relative to the horizontal "run." The slope and the intercept (b 0, here -23846) represent parameters calculated by the regression process. In the regression equation above, the b 1 term, 0.6942, represents the slope of the regression line. Suppose a regression formula is, y i = -23846 + 0.6942 x x i, where the large constant and the x terms are on a date scale for a spreadsheet program (e.g., S= 35674). In general, the regression line does not touch all the scatter points, or even many the error terms represent the differences between the actual value of Y and the regression estimate. Linear regression is a technique that finds the best straight-line fit to a set of data. The slope coefficient, b 1, measures the amount of change in Y for every one unit increase in X.Īlso note the error term, denoted by e i.It is the point at which the line cuts through the Y-axis. The Y-intercept is given by b 0 this is the value of Y when X = 0. ![]() ![]() There are two regression coefficients in this equation: The following regression equation explains the relationship between the dependent variable and independent variable: Y i = b 0 + b 1X i + e i, i = 1, 2.
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