r - 测试简单线性回归中的斜率是否等于 R 中的给定常数

Question

我想测试简单线性回归中的斜率是否等于除零以外的给定常量。

> x <- c(1,2,3,4)
> y <- c(2,5,8,13)
> fit <- lm(y ~ x)
> summary(fit)

Call:
lm(formula = y ~ x)

Residuals:
   1    2    3    4 
 0.4 -0.2 -0.8  0.6 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)  -2.0000     0.9487  -2.108  0.16955   
x             3.6000     0.3464  10.392  0.00913 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7746 on 2 degrees of freedom
Multiple R-squared:  0.9818,    Adjusted R-squared:  0.9727 
F-statistic:   108 on 1 and 2 DF,  p-value: 0.009133
> confint(fit)
                2.5 %   97.5 %
(Intercept) -6.081855 2.081855
x            2.109517 5.090483

在这个例子中，我想测试斜率是否等于 5。我知道我不会拒绝它，因为 5 在 95% CI 中。但是有没有一个函数可以直接给我 p 值？

Answer 1

您只需为零假设斜率 = 5 构建 t 统计量:

# Compute Summary with statistics      
sfit<- summary(fit)
# Compute t-student H0: intercept=5. The estimation of coefficients and their s.d. are in sfit$coefficients
tstats <- (5-sfit$coefficients[2,1])/sfit$coefficients[2,2]
# Calculates two tailed probability
pval<- 2 * pt(abs(tstats), df = df.residual(fit), lower.tail = FALSE)
print(pval)