[R] Regression fitting

The following example

> Fit <-LM (y~x, data =data01)>Summary (FIT) CALL:LM (Formula= data01$p ~ data01$m, data =data01) Residuals:min 1Q Median 3Q Max-4.2070-2.9109-0.9089  2.9160  8.8993coefficients:estimate Std. Error t value Pr (>|t|) (Intercept)6.340e+00  7.472e-01   8.485 4.26e-09***x1.305e-04  2.657e-05   4.911 3.87e-05***---signif. Codes:0‘***’0.001‘**’0.01‘*’0.05‘.’0.1‘ ’1residual standard error:3.575On -degrees of Freedommultiple R-squared:0.4718, Adjusted r-squared:0.4522F-statistic:24.11On1and -DF, P-value:3.872e-05

Coefficients:

Four values in turn are:

Estimate Std. Error t value Pr (>|t|)
Valuation, standard error, T-value, p-value

We can determine the significance of the corresponding explanatory variable directly by comparing the P value with our pre-set 0.05 (the original hypothesis is that if the coefficient is significantly 0,p<0.05, the original hypothesis is rejected, that is, the corresponding variable is significantly not 0). We can see that the intercept term intercept and X are considered to be significantly less than 0 at p 0.05, passing the significance test

Goodness of Fit r^2

We see multiple r-squared and adjusted r-squared these two values, in fact we often call "goodness of Fit" and "modified goodness of fit", refers to the regression equation to the sample fitting degree geometry, here we can see that the modified goodness of fit = 0.4522, that is, the approximate fitting degree of less than 50%, indicating that the degree of fitting is very general. This value is of course the higher the better, of course, there are many ways to improve the goodness of fit, and when it reaches a certain level, we think it is almost. In particular, there is a very complex decision content, interested can see: http://baike.baidu.com/view/657906.htm

F-statistic

We often say that f-statistic (f-test), often used to determine the overall significance of the equation test, its p-value of 3.872e-05, is obviously <0.05, we can think of the equation at p=0.05 level or through the significance of the test.

Summarize:
T test is to test the significance of explanatory variables;
R-squared is to see how the equation fits;
The F-Test is to test the overall significance of the equation;

[R] Regression fitting