 Solution

TODO: the coefficients and their numerical $t$ and $p$ entries cannot be recovered. The coefficient estimate gives a modeled difference relative to the stated reference coding; its standard error quantifies uncertainty, and the usual coefficient test uses $t=\hat{\beta }/\mathrm{SE}(\hat{\beta })$ for a zero-coefficient null hypothesis. The p-value requires the appropriate reference distribution and statistical degrees of freedom. In a conventional R coefficient table an Estimate is usually an unstandardized regression coefficient, not automatically a standardized regression coefficient; the table and model documentation must establish which meaning of $\beta$ is intended. These definitions supply no missing numerical values.