寻找差异btw。 R中的线性回归线

Question

我试图找出如何比较线性回归（线）以检查这些回归的斜率是否存在任何显着差异。

我已广泛搜索，但无法解决问题。我很感激任何帮助。

这是最小的工作示例：

# making a dataframe
x <- c(13.5, 2.8, 10.1, 5.8, 6.4, 12.5, 3.2, 8.9, 13.0)
y <- c(1.2, 3.2, 0.2, 1.9, 2.5, 0.6, 2.0, 0.4, 1.3)
z <- c("A","A","A","B","B","B","C","C","C")

df = data.frame(x, y, z)

df
#      x   y z
# 1 13.5 1.2 A
# 2  2.8 3.2 A
# 3 10.1 0.2 A
# 4  5.8 1.9 B
# 5  6.4 2.5 B
# 6 12.5 0.6 B
# 7  3.2 2.0 C
# 8  8.9 0.4 C
# 9 13.0 1.3 C

###############################################
# plotting the data
plot(log10(x) ~ log10(y), 
     col=c("blue","red","green")[unclass(z)], data = df,
     pch=20)


###############################################
# subsetting the data for making the regrssion lines
df.A <- subset(df, z == "A")
df.B <- subset(df, z == "B")
df.C <- subset(df, z == "C")

###############################################
# making and drawing the regression line for A
res.A=lm(log10(df.A$x) ~log10(df.A$y))

res.A
# Call:
#   lm(formula = log10(df.A$x) ~ log10(df.A$y))
# 
# Coefficients:
#   (Intercept)  log10(df.A$y)  
#        0.8458        -0.3862 

# drawing the regression line A
abline(res.A, col= "blue", lty = 2)


###############################################
# making and drawing the regression line for B
res.B=lm(log10(df.B$x) ~log10(df.B$y))

res.B
# Call:
#   lm(formula = log10(df.B$x) ~ log10(df.B$y))
# 
# Coefficients:
#   (Intercept)  log10(df.B$y)  
#        0.9688        -0.5271 

#drawing the regression line B
abline(res.B, col= "red", lty = 2)


###############################################
# making and drawing the regression line for C
res.C=lm(log10(df.C$x) ~log10(df.C$y))

res.C
# Call:
#   lm(formula = log10(df.C$x) ~ log10(df.C$y))
# 
# Coefficients:
#   (Intercept)  log10(df.C$y)  
#        0.8586        -0.4330  

#drawing the regression line C
abline(res.C, col= "green", lty = 2)

谢谢！

Answer 1

使用anova将具有一个斜率和3个截距的模型与具有3个斜率和3个截距的模型进行比较：

fm1 <- lm(log10(y) ~ z + log10(x), df)
fm3 <- lm(log10(y) ~ z + log10(x)/z, df)
anova(fm1, fm3)

，并提供：

Analysis of Variance Table

Model 1: log10(y) ~ z + log10(x)
Model 2: log10(y) ~ z + log10(x)/z
  Res.Df     RSS Df Sum of Sq      F Pr(>F)
1      5 0.72132                           
2      3 0.64793  2  0.073387 0.1699 0.8513

所以斜率之间的差异并不显着。

请注意，我们只有少量数据，因此差异必须足够大才能找到这样的差异。