You can see how they fit into the equation at the bottom of the results section. These parameter estimates build the regression line of best fit. The first portion of results contains the best fit values of the slope and Y-intercept terms. The interpretation of the intercept parameter, b, is, "The estimated value of Y when X equals 0." The linear regression interpretation of the slope coefficient, m, is, "The estimated change in Y for a 1-unit increase of X." X is simply a variable used to make that prediction (eq. Keep in mind that Y is your dependent variable: the one you're ultimately interested in predicting (eg. The calculator above will graph and output a simple linear regression model for you, along with testing the relationship and the model equation. Linear regression calculators determine the line-of-best-fit by minimizing the sum of squared error terms (the squared difference between the data points and the line). While it is possible to calculate linear regression by hand, it involves a lot of sums and squares, not to mention sums of squares! So if you're asking how to find linear regression coefficients or how to find the least squares regression line, the best answer is to use software that does it for you. Variables (not components) are used for estimation Have a look at our analysis checklist for more information on each: If you're thinking simple linear regression may be appropriate for your project, first make sure it meets the assumptions of linear regression listed below. 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. It is therefore important to know how to convert between various forms of linear equations to best suit the application.Ĭonverting from point-slope or slope-intercept form to standard form involves moving all the variables to one side of the equation, moving the constant to the other side, then manipulating the equation as necessary such that the coefficients of the terms of the equation are integers.Linear regression is one of the most popular modeling techniques because, in addition to explaining the relationship between variables (like correlation), it also gives an equation that can be used to predict the value of a response variable based on a value of the predictor variable. Slope-intercept and point-slope form are two commonly used forms of a linear equation that, while useful for graphing, are not useful for solving systems of linear equations. For example, when solving systems of linear equations, it is helpful to first convert the equation into standard form. Converting to standard formĭifferent forms of linear equations are useful for different applications. Thus, plotting the line doesn't require any calculation of the intercepts. Equations in slope-intercept and point-slope form include the slope of the line, and a point on the line, which can be immediately read from the equation. Once the x and y-intercepts are found, the line can be graphed by plotting the x and y-intercepts then drawing a line connecting the intercepts.ĭepending on the linear equation, it can be easier to graph a line given an equation in slope-intercept or point-slope form, since it can be tedious to calculate the x and y-intercepts given an equation in standard form. Finding the x-intercept using either of these two other forms is more tedious than it is with standard form. One of the key benefits of the standard form of a linear equation over point-slope form and slope-intercept form is the ease with which it can be used to find the x-intercept. Doing so results in the general formulas for finding the x and y-intercept given a linear equation in standard form: Standard form is useful because the x- and y-intercepts of the line can be easily found by setting x or y equal to 0, then solving for the desired variable. The standard form of a linear equation is given by the equation: In this case, standard form refers to the standard form of a linear equation. Standard form is a term commonly used to describe the most typical form of an object (like a number, expression, equation, etc.) used in a number of different topics. Home / algebra / linear equations / standard form Standard form
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