equation of least squares regression line calculator

#EQUATION OF LEAST SQUARES REGRESSION LINE CALCULATOR SERIES#

Suppose b is a 'candidate' value for the parameter vector β. Suppose the data consists of n Estimation Here the ordinary least squares method is used to construct the regression line describing this law. Main article: Linear regression model Okun's law in macroeconomics states that in an economy the GDP growth should depend linearly on the changes in the unemployment rate. Under the additional assumption that the errors are normally distributed with zero mean, OLS is the maximum likelihood estimator that outperforms any non-linear unbiased estimator. Under these conditions, the method of OLS provides minimum-variance mean-unbiased estimation when the errors have finite variances. The OLS estimator is consistent for the level-one fixed effects when the regressors are exogenous and forms perfect colinearity (rank condition), consistent for the variance estimate of the residuals when regressors have finite fourth moments and-by the Gauss–Markov theorem- optimal in the class of linear unbiased estimators when the errors are homoscedastic and serially uncorrelated. Now the computer calculates things and finds us a least-squares regression line. So imagine the data on a scatterplot, with caffeine consumed as the x-axis, and hours studying as the y-axis. x caffeine consumed and y hours studying. The resulting estimator can be expressed by a simple formula, especially in the case of a simple linear regression, in which there is a single regressor on the right side of the regression equation. We asked the computer to perform a least-squares regression analysis on some data with. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression surface-the smaller the differences, the better the model fits the data. In statistics, ordinary least squares ( OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable.

#EQUATION OF LEAST SQUARES REGRESSION LINE CALCULATOR SERIES#

Method for estimating the unknown parameters in a linear regression model Part of a series on

Equation of least squares regression line calculator