Consider the summary output of the following two regressions where the analysis is separated for the American and National leagues. (Some of the output is omitted to save space.) American League: Call: 1m(formula R[League == "American"] H[League "American"]) Coefficients: Estimate Std. Error t value Pr(>ltl) -159.1593 415.5425 -0.383 0.7084 0.2685 2.447 0.0308. (Intercept) H[League "American"] 0.6569 Signif. codes: 00.001 0.01 0.05 0.11 National League: Call: in (formula R[League "National"]H[League - "National"]) Coefficienta: NO Estimate Std. Errort value Pr(>ltl). -486.0854 233.7741 -2.079 0.0565 0.1583 5.555 7.09-05 *** (Intercept) H[League "National"] 0.8796 Signif. codes: 0 0.001 0.01 0.05 0.11 Based on these summaries, is the change in the number of runs scored for each extra hit (statistically) different in the two leagues? State your hypothesis, formally, and give the test statistic and your conclusion.