This simple linear regression calculator uses the least squares method to find the line of best fit for a set of paired data, allowing you to estimate the value of a dependent variable (Y) from a given independent variable (X).
The line of best fit is described by the equation ŷ = bX + a, where b is the slope of the line and a is the intercept (i.e., the value of Y when X = 0). This calculator will determine the values of b and a for a set of data comprising two variables, and estimate the value of Y for any specified value of X.
To begin, you need to add paired data into the two text boxes immediately below (either one value per line or as a comma delimited list), with your independent variable in the X Values box and your dependent variable in the Y Values box. For example, if you wanted to generate a line of best fit for the association between height and shoe size, allowing you to predict shoe size on the basis of a person's height, then height would be your independent variable and shoe size your dependent variable).
This calculator can estimate the value of a dependent variable (Y) for any specified value of an independent variable (X). Simply add the X values for which you wish to generate an estimate into the Estimate box below (either one value per line or as a comma delimited list).
Note: If you just want to generate the regression equation that describes the line of best fit, leave the box below blank.
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.
To calculate the Linear Regression (ax+b): Press [STAT] to enter the statistics menu.Press the right arrow key to reach the CALC menu and then press 4: LinReg(ax+b).
The equation is in the form of “Y = a + bX”. You may also recognize it as the slope formula. To find the linear equation by hand, you need to get the value of “a” and “b”.Then substitute the resulting value in the slope formula and that gives you your linear regression equation.
A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).
The equation which defines the simplest form of the regression equation with one dependent and one independent variable: y = mx+c. Where y = estimated dependent variable, c = constant, m= regression coefficient and x = independent variable.
Next to calculate the Linear Regression (ax+b): 1) First press the [STAT] key to enter the statistics menu.2) Then press the [right arrow] key to reach the CALC menu and then press the [4] key to select LinReg(ax+b).
We could use the equation to predict weight if we knew an individual's height. In this example, if an individual was 70 inches tall, we would predict his weight to be: Weight = 80 + 2 x (70) = 220 lbs. In this simple linear regression, we are examining the impact of one independent variable on the outcome.
This analysis technique uses one variable to predict the value of another variable. The standard formula is written as y= x+b, where y is what you're trying to find, x is the variable the outcome depends on, and b is the value if your activity is zero.
Simple linear regression is used to estimate the relationship between two quantitative variables. You can use simple linear regression when you want to know: How strong the relationship is between two variables (e.g., the relationship between rainfall and soil erosion).
Simple linear regression. In the simplest case, the regression model allows for a linear relationship between the forecast variable y and a single predictor variable x : yt=β0+β1xt+εt.
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