Test for significance of coefficient in ols regression

Hi all,

Suppose i have the following fictional df:

df <- data.frame(
Company = rep(LETTERS[1:10], each = 10),
Year = rep(2010:2019, times = 10),
Var1 = runif(100, -1, 1),
Var2 = runif(100, -1, 1),
Var3 = runif(100, -1, 1),
Var4 = runif(100, -1, 1),
Var5 = runif(100, -1, 1)
)

summary(ls1 <- lm(Var1 ~ Var2 + Var3 + Var4 + Var5, data=df))

I want to test whether the coefficient of Var 3 significantly is different from zero at significance level of pvalue of 0.01 , or if it not (so equal to 0). If it is different from zero, i would like to know whether the coefficient is then > 0 or < 0.

Moreover, i want to test whether also whether the coefficient of Var5 bigger or smaller than the coefficient of Var4 at a level of 0.01, or whether the coefficient of Var5 does not differ significantly from the coefficient from Var4 (so Var5 = Var4 at significance level of P value < 0.01).

Any help would be highly appreciated. I am still new to R so i do not understand this completely.

The first question is easy. You want a "one-tailed" test rather than a "two-tailed" test. For example, if you want the one-tailed critical value at the 5 percent level with 95 degrees of freedom use qt(0.05,1000).

To test hypotheses involving multiple coefficients take a look at linearhypothesis in the car package. Some guidance is given at Linear Hypothesis Tests | LOST

How do you understand the meaning of a coefficient of a variable set as an independent variable in linear regression? Visualize the model.

# for reproducibility; otherwise each time
# data frame is generated, values are very
# likely to differ
set.seed(42)
d <- data.frame(
  Company = rep(LETTERS[1:10], each = 10),
  Year = rep(2010:2019, times = 10),
  Var1 = runif(100, -1, 1),
  Var2 = runif(100, -1, 1),
  Var3 = runif(100, -1, 1),
  Var4 = runif(100, -1, 1),
  Var5 = runif(100, -1, 1)
)

# simplify for illustration

fit <- lm(Var1 ~ Var3, data = d)
summary(fit)
#> 
#> Call:
#> lm(formula = Var1 ~ Var3, data = d)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -1.15316 -0.56749 -0.01864  0.49949  0.98071 
#> 
#> Coefficients:
#>             Estimate Std. Error t value Pr(>|t|)
#> (Intercept)  0.06090    0.06171   0.987    0.326
#> Var3         0.10085    0.10602   0.951    0.344
#> 
#> Residual standard error: 0.6042 on 98 degrees of freedom
#> Multiple R-squared:  0.009147,   Adjusted R-squared:  -0.0009637 
#> F-statistic: 0.9047 on 1 and 98 DF,  p-value: 0.3439
# visualize
library(ggplot2)
ggplot(d,aes(Var1,Var3)) + 
  geom_smooth(method = "lm") +
  theme_minimal() +
  geom_hline(yintercept = coef(fit)[1], color = "red")
#> `geom_smooth()` using formula = 'y ~ x'

Created on 2023-05-30 with reprex v2.0.2

What part of the plot represents the coefficient? What part represents a coefficient of zero? Is there a difference? What would cause someone to doubt that the difference was not simply the result of random variation?

This topic was automatically closed 42 days after the last reply. New replies are no longer allowed.

If you have a query related to it or one of the replies, start a new topic and refer back with a link.