利用R语言进行线性/非线性回归拟合实例（1）

利用R语言进行线性/非线性回归拟合实例（1）

1、 生成一组数据

vectorxxvec;

vectoryyvec;

 

                ofstreamfout("data2.txt");

                for (int i =1;i<200;i++)

                {

                                  float x =i*0.8;

                                  float randdnum= rand()%10 * 10;

                                  floatrandomflag = (rand()%10)%2==0?(1):(-1);

                                  float y = 3 *x*x + 2*x + 5 + randomflag*randdnum;

                                  fout<

                                  xxvec.push_back(x);

                                  yyvec.push_back(y);

                }

                    fout.close();

将生成的数据存为txt文件，命名为“data1”

 

2、线性拟合

#-------------------------------------------------------------#载入数据

> fire <- read.table('D:/data.txt',header = TRUE)

#-------------------------------------------------------------#回归分析

> plot(fire$y ~ fire$x)

> fire.reg <- lm(fire$y ~ fire$x,data = fire) #回归拟合

> data1.reg

Call:

lm(formula = data1$y ~ data1$x, data = data1)

Coefficients:

(Intercept)      data1$x 

6.202       3.003 

 

>summary(data1.reg) #回归分析表

Call:

lm(formula = data1$y ~ data1$x, data = data1)

Residuals:

    Min      1Q Median      3Q     Max

-93.345 -42.929  -1.948  46.717 88.793

 

Coefficients:

            Estimate Std. Error tvalue Pr(>|t|)   

(Intercept)  6.202084   3.352055    1.85  0.0646 . 

data1$x     3.002826  0.007259  413.66  <2e-16 ***

标红数字即为线性回归系数，由于生成数据时加了一个随机数，所以拟合出来的直线为：

y=3.002826 x+6.202084  

---

Signif. codes:  0 ‘***’ 0.001 ‘**’0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 52.93 on 997 degrees of freedom

Multiple R-squared:  0.9942,         Adjusted R-squared:  0.9942

F-statistic: 1.711e+05 on 1 and 997 DF, p-value: < 2.2e-16

 

>anova(data1.reg) #方差分析表

Analysis of Variance Table

Response: data1$y

           Df    Sum Sq  Mean Sq F value    Pr(>F)   

data1$x     1479462873 479462873  171112 < 2.2e-16***

Residuals 997  2793641      2802                     

Signif. codes:  0‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

 

>abline(data1.reg, col = 2, lty = 2) #拟合直线