# Linear Regression - (Feb/26/2008 )

Can some body explain me what is linear regression. or this graph.

1> Correlation plot of normalized second responses versus current density from CHO-K1 cells expressing wild-type VR1 either transiently (open

circles, n =37) or stably (filled circles, n =21). The straight line is a linear regression fit to all of the wild-type data points with an r2 0.34.

2> VR1 aspartate mutants plotted against regression line describing relationship of desensitization versus current density for wild-type VR1 as defined in Figure 4C.

linear regression is an attempt to fit data into a straight line.

r2 is the correlation coefficient. r2=1.0000 is a perfect fit of the data to a straight line. r2>0.9 is okay but we like to see 0.98 or better for standard curves. r2=0.34 is a poor fit (although, not too bad for a scatter plot like yours).

thanks for your explanation but i want to know more.

WHere there is need to produce the straingt line and what information one can get from this straight line and second if the angle of this line is changed or this line is in different direction then what will happened.

r2 is the correlation coefficient. r2=1.0000 is a perfect fit of the data to a straight line. r2>0.9 is okay but we like to see 0.98 or better for standard curves. r2=0.34 is a poor fit (although, not too bad for a scatter plot like yours).

You have two variables, a dependent variable on the X axis, that you know its values (eg time, concentration,...) and the other is an independent variable (Y axis) and there are your experimental results.

If there is a direct relationship or viceversa, over time more or less the response, r-coeficient from your linear regression will be your best, with a high value close to 1. If there is no relationship, your coeficient line ® will be badm, with values far from 1

I hope you serve

my response to your first question is more philosophical than scientific. data that gives a straight line is easier to understand (and the math is simpler) than data that gives a curve or shows no simple trend. we try to fit all data to a simple linear equation (y=mx+b) before trying some other equation. hence, we only consider the linear portions of standard curves as valid and set the limits of the determination on this basis. this is not necessarily a wrong attitude. remember the "kis" rule (keep it simple). the simplest solution is usually the correct solution.

for your second question, the angle (slope) of the line tells you the dose effect of the fixed variable. in your examples, an increase in initial response seems to cause a decrease in secondary response. the slope tells you how "fast" the change occurs (dy/dx). the direction of the slope (up or down, + or -) tells you whether the response is positive or negative (your case is negative).