(d) 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: Ca11: 1m( formula =R[ League == "American"] H[ League == "American"]) Coefficients: \begin{tabular}{l|rrrr|} & Estimate & Std, Error t value Pr(>t) \\ (Intercept) & 159.1593 & 415.5425 & 0.383 & 0.7084 \\ H[League = "American"] & 0.6569 & 0.2685 & 2.447 & 0.0308 \end{tabular} Signtf, codes: 0 '**' 0.001 '*' 0.01 *' 0.05 '. 0.1 ' 1 National League: Cal1: lm( formula =R[ League = "National"] H[ League = " "National"]) Coefticienta: Signif, codes: 0 '**' 0.001 '*' 0.01 '*' 0.05 ':l 0.1 ' 0.1 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. (d) 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: Ca11: 1m( formula =R[ League == "American"] H[ League == "American"]) Coefficients: \begin{tabular}{l|rrrr|} & Estimate & Std, Error t value Pr(>t) \\ (Intercept) & 159.1593 & 415.5425 & 0.383 & 0.7084 \\ H[League = "American"] & 0.6569 & 0.2685 & 2.447 & 0.0308 \end{tabular} Signtf, codes: 0 '**' 0.001 '*' 0.01 *' 0.05 '. 0.1 ' 1 National League: Cal1: lm( formula =R[ League = "National"] H[ League = " "National"]) Coefticienta: Signif, codes: 0 '**' 0.001 '*' 0.01 '*' 0.05 ':l 0.1 ' 0.1 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