Linear function Fitting R Language Example _r language

Linear function fitting (Y=A+BX)

1. R Run Instance

The R language runs the code as follows: Green for the data to be provided, the yellow identification information is required to be saved.

X<-c (0.10,0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.20, 0.21, 0.23)

Y<-c (42.0,43.5, 45.0, 45.5, 45.0, 47.5, 49.0, 53.0, 50.0, 55.0, 55.0, 60.0)

Data1=data.frame (x=x,y=y) #数据存入数据框

#拟合线性函数

LM.DATA1<-LM (y~ x,data=data1)

Summary (LM.DATA1) #输出拟合后信息

Call:

LM (formula = data1$y ~ data1$x)

Residuals: #残差分位数 (all residual values are shown here when the number of residuals is low)

Min 1Q Median 3Q Max

-2.0431-0.7056 0.1694 0.6633 2.2653

Coefficients:

#系数估计值 #系数标准误差 #t检验值 #对应t值概率的2倍

Estimate Std. Error T value Pr (>|t|)

(Intercept) 28.493 1.580 18.04 5.88e-09 * * *

data1$x 130.835 9.683 13.51 9.50e-08 * * *

---

Signif. codes:0 ' * * * 0.001 ' * * ' 0.01 ' * ' 0.05 '. ' 0.1 "' 1

Residual standard error:1.319 on 10degrees of Freedom

#拟合优度判定系数 #修正的拟合优度判定系数

Multiple r-squared:0.9481, adjustedr-squared:0.9429

#F检验值 #F检验值对应的概率

f-statistic:182.6 on 1 and DF, p-value:9.505e-08

T-Test value corresponds to PR (>|t|) : This number is twice times the probability of T-test, so its value is less than 0.1, it shows that the corresponding independent variable is significant for the variable, of course, the smaller the value, the higher the significance.

F test value corresponding to the P-VALUE:F test value of the corresponding probability. When the value is less than 0.05, the regression equation is significant.

Adjusted r-squared modified fitting: The closer the value is to 1, the better the model fits.

/*********************** Numerical output ********************************/

Coefficient<-lm.data1$coefficients #回归所有系数列举

COEFFICIENT[1] #系数a: Intercept

coefficient [2] #系数b

Tvalue<-summary (lm.data1) $coefficients [1:2,3] #t检验值

TVALUE[1] #系数a对应的t检验值

TVALUE[2] #系数b对应的t检验值

Pr<-summary (lm.data1) $coefficients [1:2,4] #t检验值对应的概率的2倍

PR[1] #系数a对应t检验值对应的概率2倍

PR[2] #系数b对应t检验值对应的概率2倍

Arsquared<-summary (LM.DATA1) $adj. r.squared #修正的拟合优度判定系数

F_info<-summary (lm.data1) $fstatistic #F检验的F值, degrees of freedom DF and probability

F_INFO[1] #F检验值

F_INFO[2] #F检验量的自由度

F_INFO[3] #F检验值对应的概率

/****************************************************************/

#残差正态性检验

Ks.test (Lm.data1$residuals, "Pnorm", 0)

One-samplekolmogorov-smirnov Test

Data:lm.data1$residuals

#D检验值 #对应的概率值

D = 0.1332, P-value = 0.9648

Alternative hypothesis:two-sided

The probability value corresponding to the D test value is P-value: The value is greater than 0.05, indicating that the residuals obey the normal distribution with the mean value of 0.

/*********************** Numerical output ********************************/

Ks_test<-ks.test (Lm.data1$residuals, "Pnorm", 0) #获取正态性检验信息

KS_TEST[1] #KS检验值

KS_TEST[2] #KS检验值对应的概率

/****************************************************************/

#残差独立性检验: DW method to test the autocorrelation of residual error sequences

Dwtest (LM.DATA1)

Durbin-watsontest

Data:lm.data1

#d. W Test Value # corresponding to the probability value

DW = 2.5465, P-value = 0.7422

Alternative hypothesis:trueautocorrelation is greater than 0

DW test value corresponding to the probability value P-value: This value is greater than 0.05, the residual sequence is independent.

/*********************** Numerical output ********************************/

Dw_test<-dwtest (LM.DATA1) #获取独立性检验信息

DW_TEST[1] #DW检验值

DW_TEST[4] #DW检验值对应的概率

/****************************************************************/

#残差同方差检验

Bptest (LM.DATA1)

Studentizedbreusch-pagan Test

Data:lm.data1

#BP检验值 #自由度 #对应概率值

BP = 0.9831, df = 1, P-value = 0.3214

The probability value of the BP test value is P-value: The value is greater than 0.05, which indicates that the residual difference is the same variance.

/*********************** Numerical output ********************************/

bp_test<-bptest (lm.data1) #获取独立性检验信息

BP_TEST[1] #BP检验值

BP_TEST[2] #BP检验量的自由度

BP_TEST[4] #BP检验值对应的概率

/****************************************************************/

2. Curve Fitting

Ab<-round (lm.data1$coefficients[1],3) #回归方程系数a, retain 3 decimal places

Bb<-round (lm.data1$coefficients[2],3) #回归方程系数b, retain 3 decimal places

Plot (data1$x,data1$y,xlab= "x", Ylab = "Y", col= "Red", pch= "*") #训练数据点

Abline (lm.data1,col= "Blue") #拟合曲线

Text (mean (data1$x), Max (data1$y), paste ("y =", BB, "x+ (", AB, ")", Sep = "") #方程式