If we type lm.fit, some basic information about the model is output.

> lm.fit
Call:
lm(formula = medv ~ lstat)
Coefficients:
(Intercept ) lstat
      34.55  -0.95

For more detailed information, we use summary(lm.fit). This gives us p-values and standard errors for the coefficients, as well as the R² statistic and F-statistic for the model.

> summary (lm.fit)
Call:
lm(formula = medv ~ lstat)
Residuals :
   Min      1Q  Median   3Q   Max
-15.17   -3.99   -1.32 2.03 24.50
Coefficients:
             Estimate   Std. Error   t value    Pr(>|t|)
(Intercept)   34.5538       0.5626      61.4      <2e-16 ***
lstat         -0.9500       0.0387     -24.5      <2e-16 ***
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
Residual standard error: 6.22 on 504 degrees of freedom
Multiple R-squared: 0.544, Adjusted R-squared: 0.543
F-statistic : 602 on 1 and 504 DF, p-value: <2e-16

There is much to dissect in this summary. Firstly, the call that was used to create the regression model.

Call:
lm(formula = medv ~ lstat)

Some information about the residuals.

Residuals :
   Min      1Q  Median   3Q   Max
-15.17   -3.99   -1.32 2.03 24.50

This is our regression equation:

\[{medv} = \beta_{0} + \beta_{1} {lstat}\]

Below we can find the value for \(\beta_{0}\) and \(\beta_{1}\) being 34.5538 and -0.9500. This gives us:

\[{medv} = 34.5538 - 0.9500 {lstat}\]

Additionally, we are also given the standard error, t-values and p-values of every coefficient in our model. We can conclude that both the intercept and lstat are significant (p < 0.05).

Coefficients:
             Estimate   Std. Error   t value    Pr(>|t|)
(Intercept )  34.5538       0.5626      61.4      <2e-16 ***
lstat         -0.9500       0.0387     -24.5      <2e-16 ***

To make it simpler for us, R also uses significance codes. One * tells us that the p-value is smaller than 0.05. ** and *** means p-values smaller than 0.01 and 0.001 respectively. In our case both of our p-values are close to 0, with both being smaller than \(2*10^{-16}\).

The \(R^2\) of our model is 0.544 and \(\bar{R}^2\) is 0.543

Multiple R-squared: 0.544, Adjusted R-squared: 0.543

Lastly, to see if our model in general has any explanatory power over our dependent variable, we can use the F-statistic.

F-statistic : 602 on 1 and 504 DF, p-value: <2e-16

Here we can reject H0 that the fit of the full model equals the fit of the null model (p < 0.05).