By default lm
summary test slope coefficient equal to zero. My question is very basic. I want to know how to test slope coefficient equal to non-zero value. One approach could be to use confint
but this does not provide p-value. I also wonder how to do one-sided test with lm
.
ctl <- c(4.17,5.58,5.18,6.11,4.50,4.61,5.17,4.53,5.33,5.14)
trt <- c(4.81,4.17,4.41,3.59,5.87,3.83,6.03,4.89,4.32,4.69)
group <- gl(2,10,20, labels=c("Ctl","Trt"))
weight <- c(ctl, trt)
lm.D9 <- lm(weight ~ group)
summary(lm.D9)
Call:
lm(formula = weight ~ group)
Residuals:
Min 1Q Median 3Q Max
-1.0710 -0.4938 0.0685 0.2462 1.3690
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 5.0320 0.2202 22.850 9.55e-15 ***
groupTrt -0.3710 0.3114 -1.191 0.249
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.6964 on 18 degrees of freedom
Multiple R-squared: 0.07308, Adjusted R-squared: 0.02158
F-statistic: 1.419 on 1 and 18 DF, p-value: 0.249
confint(lm.D9)
2.5 % 97.5 %
(Intercept) 4.56934 5.4946602
groupTrt -1.02530 0.2833003
Thanks for your time and effort.
as @power says, you can do by your hand. here is an example:
> est <- summary.lm(lm.D9)$coef[2, 1]
> se <- summary.lm(lm.D9)$coef[2, 2]
> df <- summary.lm(lm.D9)$df[2]
>
> m <- 0
> 2 * abs(pt((est-m)/se, df))
[1] 0.2490232
>
> m <- 0.2
> 2 * abs(pt((est-m)/se, df))
[1] 0.08332659
and you can do one-side test by omitting 2*
.
UPDATES
here is an example of two-side and one-side probability:
> m <- 0.2
>
> # two-side probability
> 2 * abs(pt((est-m)/se, df))
[1] 0.08332659
>
> # one-side, upper (i.e., greater than 0.2)
> pt((est-m)/se, df, lower.tail = FALSE)
[1] 0.9583367
>
> # one-side, lower (i.e., less than 0.2)
> pt((est-m)/se, df, lower.tail = TRUE)
[1] 0.0416633
note that sum of upper and lower probabilities is exactly 1.
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