# 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 ?
A plot of the mean scores corresponding to each Process Standard over the 14 semesters is shown, along with the line of best fit, in Figure 3.
A nonlinear optimizer (GAMS 2.25, 1992) was configured to find the curved line of best fit based on LAD.
In each case, LAD produced the superior line of best fit, although the degree of improvement was generally small.
Move to the right end of the x-axis on graph 1 (for longer duration of exercise) and then move up to the line of best fit. The resulting point correlates to a large amount of muscle energy required (the dependent variable).
Staying with the large value for muscle energy from graph 1, we look to the right on graph 2 (muscle energy now being the independent variable), and then move up to the line of best fit. The resulting point correlates to a high level of glucose uptake by the muscles.
The students pointed out that using graphical representation enabled them to interpolate data by approximating a line of best fit. For instance, from the line they found that one could see 30.4 centimetres if positioned 2.2 metres from the wall.
They noted that the TI-84 would calculate a line of best fit; thus, they would not have to find it from their byhand plot of the data (Figure 2).
(Note that the correlation coefficient, or [R.sup.2], for the PCL in this example is 0.9397, showing excellent correlation between the data and the line of best fit, or PCL.
1B) showed excellent correlation ([r.sup.2] = 0.96, [S.sub.y|x] = 0.80), and the line of best fit was not significantly different from the line of identity: slope 0.947 (95% confidence interval 0.91-1.02); y-intercept 0.23 (0.520.97).
When I plotted the data on a graph and drew a line of best fit, the equation for it was Y = X.
The line of best fit was obtained by multiplying the difference in ranking points by somewhere between 0.007 and 0.008 and allowing half a goal for home advantage, where appropriate.

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