test if slope is significantly different than 8 in r

To test if slope is significantly different than 8 in R, we can perform a hypothesis test using linear regression. Our null hypothesis is that the slope equals 8, while the alternative hypothesis is that the slope does not equal 8.

main.r
# Generate sample data
set.seed(123)
x <- rnorm(100)
y <- 8 + 2*x + rnorm(100)

# Perform linear regression
lm_model <- lm(y ~ x)

# Perform hypothesis test
summary(lm_model)
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The output of the summary() function shows the estimated slope and intercept coefficients, as well as their standard errors, t-values, and p-values. We can see that the estimated slope coefficient is 1.935, which is not equal to 8. The corresponding t-value is 9.949, and the p-value is less than 0.001. This means we can reject the null hypothesis and conclude that the slope is significantly different than 8 at a significance level of 0.05.