= Solution
The command performs a <nested-model F-test> for $H_0:\beta_1=0$ against $H_1:\beta_1\ne0$, retaining the intercept and $x_2$ coefficient in both models. Write $RSS_2$ and $RSS_3$ for the <residual sum of squares> in the reduced and full fits. Under $H_0$ and the independent normal-error assumptions,
$$
\boxed{F=\frac{(RSS_2-RSS_3)/1}{RSS_3/(n-3)}\sim F_{1,n-3},\qquad p=\Pr(F_{1,n-3}\geq F_{obs}).}
$$
By <Cochran's theorem>, the numerator and denominator are independent scaled chi-squares with one and $n-3$ degrees of freedom. Equivalently, for this single-coefficient restriction, $F=t_{\beta_1}^2$, so its p-value equals that of the two-sided coefficient <Student's t-test> in model3.
Using the printed $t$ value gives $F=0.800^2=0.640$ and $p\approx0.43$. The printed estimate and standard error instead give
$$
\boxed{F=(1.8663/2.3538)^2\approx0.62867,\qquad p\approx0.43.}
$$
This discrepancy is present in the PDF and is too large to be explained by rounding at the shown precision; the underlying ANOVA output is omitted, so an exact unique statistic cannot be recovered. The univariate correlation and $t$ value imply $n\approx2+2.575^2(1-0.2517297^2)/0.2517297^2\approx100.006$, consistent with $n=100$ after rounding. With denominator degrees of freedom 97, the two versions give p-values approximately $0.4257$ and $0.4298$, respectively. Either way the partial effect is not significant at 5%.
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