# linear regression

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## linear regression

A statistical method defined by the formula y = mx = b which is used to "best-fit" straight lines to scattered data points of paired values Xi, Yi, where the values of Y—the ordinate or vertical line—are “observations” or values of a variable (e.g., systolic blood pressure) and the values of X—the abscissa or horizontal line—increased in a relatively nonrandom fashion (e.g., age). Linear regression is a parametric procedure for determining the relationship between one or more (multiple) continuous or categorical predictor (or independent) variables and a continuous outcome (or dependent) variable.

In the equation y = mx = b:
m = slope
b = y - intercept

## linear regression

Statistics A statistical method defined by the formula y = a + bx, which is used to 'fit' straight lines to scattered data points of paired values Xi, Yi, where the values of Y–the ordinate or vertical line are observations of a variable–eg, systolic BP and the values of X–the abscissa or horizontal line ↑ in a relatively nonrandom fashion–eg, age
McGraw-Hill Concise Dictionary of Modern Medicine. © 2002 by The McGraw-Hill Companies, Inc.

## linear regression

A statistical method of predicting the value of one variable, given the other, in a situation in which a CORRELATION is known to be significant. The equation is y = a + bx in which x and y are, respectively, the independent and dependent variables and a and b are constants. This is an equation for a straight line.
Collins Dictionary of Medicine © Robert M. Youngson 2004, 2005
References in periodicals archive ?
Use of several statistical methods has been adopted such as multiple linear regressions, Pearson correlation, simple regression, nonlinear regression etc.
Scott, "Multiple Linear Regression Analysis: a matrix approach in MATLAB," Alabama Journal of Mathematics, Spring/ Fall2009,3 pages, 2009.
After the establishment of multiple linear regression model, the images from training libraries are placed into the multiple linear regression model; then the disease recognition system is constructed by using the least squares method.
The variables selected via StepWise were used to determine the multiple linear regression equation, for the simulation of wheat biomass yield to generate an equation of the following type:
This implies that per capita income variable as a whole can be explained by the variable of GRDP at CMV, GRDP at CP and Total Population/life.The result of the analysis of multiple linear regression model of table 1 is obtained by the following equation:
Table 2 also shows the multiple linear regression model summary and overall fit statistics.
In the analysis model of multiple linear regression, variables Y, [X.sub.1], [X.sub.2], ..., [X.sub.m] are quantitative, measured in interval and relative scales, or dichotomous, of m values.
To illustrate the multiple linear regression model, we will use the hypothetical example of a nursery and retail store specializing in house and garden plants and supplies.
Squares 1 Regression 87.102 3 29.034 201.100 0.000 Residual 68.146 472 0.144 Total 55.248 475 Table 5: Multiple Linear Regression Analysis Model Unstandardizcd Standardized t p-value R Coefficient Cuefficient Beta Beta (Constant) 0.014 0.077 0.939 ATT 0.535 15.003 0.000 0.745 SN 0.159 0.189 5.398 0.000 PBC 0.200 0.185 5.002 0.000 Model R Square Std.
When I added a covariate to the spreadsheets 11 years ago (Hopkins, 2006a) to allow adjustment for a modifying subject characteristic, I acknowledged in the article that "extending the analysis to two or more covariates is simple in theory, but it is practically impossible in Excel because of the bizarre awkwardness of the LINEST function (which performs the necessary multiple linear regression)." I have now solved this problem by getting the user of the spreadsheet to specify only one effect at a time, using a row of weighting factors to combine the repeated measurements into a single "custom" effect.

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