After fitting a linear model, in it's summary we can observe coefficients estimates end some statistics about them:
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.85600 0.25078 7.401 9.85e-12 ***
Sepal.Width 0.65084 0.06665 9.765 < 2e-16 ***
Petal.Length 0.70913 0.05672 12.502 < 2e-16 ***
Petal.Width -0.55648 0.12755 -4.363 2.41e-05 ***
I learned that t value
is Estimate
/ Std. Error
. However, the formula for one-sample t-value is:
$t=\frac{\bar{x}-μ}{s_\bar{x}}$
$s_\bar{x}$ is the Std. Error
which means that $\bar{x}-μ$ must be the Estimate
. This is where I got lost. To my understanding the Estimate
is the fraction in which given variable contributes to the output. How is it equal to the difference between sample mean and expected mean? What is the expected mean in this case anyway?