##      (Intercept)          logsqft              bed   cityLong Beach 
##       5.13068374       1.20728946      -0.03010432      -0.88279791 
## citySanta Monica     cityWestwood 
##      -0.09416103      -0.46244082

• Each coefficient/slope/estimate represents the expected increase in the \(y\) that is associated with an increase in the \(x\) by one with other variables held constant.
• Said another way, if we control for the other variables, a one unit increase in \(x_i\) is associated with a \(\beta_i\) increase in the \(y\), on average.
• Being able to control for other variables is the great strength of regression.

CIs and H tests require knowledge of the sampling distribution of \(\beta\). Once transformed, each \(\beta_i\) follows a t-distribution.

\[ T = \frac{\hat{\beta} - \beta}{SE(\hat{\beta})} \sim t_{n - p - 1} \]

summary(m1)$coef

##                     Estimate Std. Error    t value      Pr(>|t|)
## (Intercept)       5.13068374 0.21201337  24.199812 2.164016e-110
## logsqft           1.20728946 0.03035747  39.769109 1.354681e-240
## bed              -0.03010432 0.01283644  -2.345224  1.913817e-02
## cityLong Beach   -0.88279791 0.03466805 -25.464310 3.146601e-120
## citySanta Monica -0.09416103 0.04022267  -2.340994  1.935564e-02
## cityWestwood     -0.46244082 0.04875868  -9.484276  8.562213e-21