Lab 2 Batter Up.pdf - Batter Up Lab Questions 1 Yes the...

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Unformatted text preview: Batter​ ​Up​ ​Lab​ ​Questions 1. Yes,​ ​the​ ​number​ ​of​ ​at-bats​ ​can​ ​predict​ ​the​ ​number​ ​of​ ​runs​ ​a​ ​team​ ​will​ ​score.​ ​The​ ​graph shows​ ​an​ ​overall​ ​positive​ ​association​​ ​between​ ​at-bats​ ​and​ ​runs,​ ​although​ ​the​ ​strength​ ​is not​ ​very​ ​strong.​ ​It​ ​cannot​ ​predict​ ​the​ ​exact​ ​number​ ​of​ ​runs,​ ​but​ ​can​ ​give​ ​us​ ​a​ ​rough​ ​idea. 2. The​ ​relationship​ ​between​ ​runs​ ​and​ ​at-bats​ ​is​ ​linear​,​ ​because​ ​the​ ​residual​ ​plot​ ​shows​ ​a random​ ​scatter​ ​around​ ​0,​ ​and​ ​there​ ​is​ ​no​ ​apparent​ ​patterns​ ​as​ ​the​ ​number​ ​of​ ​at-bats increases. 3. If​ ​I​ ​had​ ​to​ ​summarize​ ​my​ ​graph​ ​with​ ​a​ ​singer​ ​line,​ ​I​ ​would​ ​place​ ​it​ ​where​ ​the​ ​data​ ​points are​ ​clustered,​ ​and​ ​where​ ​the​ ​distances​ ​between​ ​the​ ​points​ ​and​ ​the​ ​line​ ​are​ ​minimized.​ ​As​ ​I move​ ​the​ ​line​ ​to​ ​better​ ​fit​ ​the​ ​date,​​ ​the​ ​sum​ ​of​ ​squares​ ​becomes​ ​smaller​ ​and​ ​smaller. This​ ​decrease​ ​in​ ​the​ ​sum​ ​of​ ​squares​ ​is​ ​due​ ​to​ ​the​ ​decreased​ ​distance​ ​between​ ​the data​ ​points​ ​and​ ​the​ ​regression​ ​line. 4. The​ ​sum​ ​of​ ​squares​ ​for​ ​the​ ​line​ ​I​ ​chose​ ​in​ ​Question​ ​3​ ​is​ ​128400,​ ​and​ ​for​ ​the​ ​least​ ​squares line​ ​is​ ​123700.​ ​The​ ​sum​ ​of​ ​squares​ ​is​ ​smaller​ ​for​ ​the​ ​least​ ​squares​ ​line​ ​because​ ​it​ ​is the​ ​closest​ ​prediction.​​ ​My​ ​prediction​ ​is​ ​not​ ​quite​ ​accurate,​ ​but​ ​is​ ​fairly​ ​close. 5. The​ ​equation​ ​to​ ​predict​ ​the​ ​number​ ​of​ ​runs​ ​is​ ​runs=0.6305(at-bats)−2790​. ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​runs=0.6305(at-bats)−2790 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​=0.6305(5508)-2790 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​=683 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Chicago​ ​Error:​ ​654-683=​ ​-29 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Cleveland​ ​Error:​ ​704-683=​ ​21 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Florida​ ​Error:​ ​625-683=​ ​-58 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Angels​ ​Error:​ ​667-683=​ ​-16 ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Typical​ ​Error:​ ​(-29+21-58-16)/4=​ ​-20.5 6. I​ ​think​ ​the​ ​number​ ​of​ ​hits​ ​would​ ​have​ ​the​ ​lowest​ ​sum​ ​of​ ​squares.​ ​From​ ​my​ ​limited understanding​ ​of​ ​baseball​ ​rules,​ ​the​ ​more​ ​hits​ ​you​ ​score,​ ​the​ ​more​ ​runs​ ​you​ ​will​ ​likely score,​ ​because​ ​hits​ ​can​ ​be​ ​stretched​ ​to​ ​runs.​ ​The​ ​graph​ ​shows​ ​a​ ​linear​ ​relationship between​ ​runs​ ​and​ ​hits,​ ​and​ ​it​ ​seems​ ​to​ ​be​ ​stronger​ ​than​ ​the​ ​relationship​ ​between​ ​runs​ ​and at-bats. 7. The​ ​slope​ ​is​​ ​0.6305​.​ ​The​ ​slope​ ​means​ ​that​​ ​for​ ​every​ ​additional​ ​number​ ​of​ ​at-bat,​ ​the number​ ​of​ ​runs​ ​is​ ​expected​ ​to​ ​increase​ ​by​ ​0.6305​.​ ​For​ ​the​ ​second​ ​graph,​ ​the​ ​slope​ ​is 0.759,​ ​which​ ​means​ ​for​ ​every​ ​additional​ ​number​ ​of​ ​hits,​ ​the​ ​number​ ​of​ ​runs​ ​is expected​ ​to​ ​increase​ ​by​ ​0.759. 8. For​ ​the​ ​graph​ ​predicting​ ​runs​ ​with​ ​at-bats,​ ​the​ ​r²​ ​value​ ​is​ ​0.37​.​ ​For​ ​the​ ​graph​ ​predicting runs​ ​with​ ​hits,​ ​the​ ​r²​ ​value​ ​is​ ​0.64​.​ ​The​ ​r²​ ​value​ ​gives​ ​the​ ​percentage​ ​of​ ​the​ ​variance​ ​of y​ ​explained​ ​by​ ​x​.​ ​Therefore,​ ​the​ ​number​ ​of​ ​hits​ ​better​ ​predict​ ​runs​ ​compare​ ​to​ ​at-bats, because​ ​64%​ ​of​ ​the​ ​variance​ ​in​ ​runs​ ​is​ ​explained​ ​by​ ​hits,​ ​while​ ​only​ ​37%​ ​of​ ​the​ ​variance in​ ​runs​ ​is​ ​explained​ ​by​ ​at-bats. 9. The​ ​number​ ​of​ ​total​ ​bases​ ​best​ ​predicts​ ​runs.​ ​Looking​ ​at​ ​the​ ​scatter​ ​plot​ ​graph,​ ​the​ ​two variables​ ​have​ ​a​ ​relatively​ ​strong​ ​linear​ ​relationship.​ ​The​ ​residual​ ​plot​ ​also​ ​tells​ ​us​ ​that it’s​ ​a​ ​good​ ​prediction,​ ​because​ ​the​ ​points​ ​are​ ​relatively​ ​close​ ​to​ ​0​ ​and​ ​are​ ​randomly scattered​ ​with​ ​no​ ​apparent​ ​pattern.​ ​The​ ​sum​ ​of​ ​squares​ ​is​ ​22070,​ ​which​ ​is​ ​much​ ​smaller than​ ​the​ ​previous​ ​graphs.​ ​The​ ​r^2​ ​value​ ​is​ ​0.89,​ ​which​ ​means​ ​that​ ​89%​ ​of​ ​the​ ​variance in​ ​runs​ ​is​ ​explained​ ​by​ ​total​ ​bases.​​ ​All​ ​these​ ​evidence​ ​tell​ ​us​ ​that​ ​total​ ​bases​ ​is​ ​a​ ​good predictor​ ​of​ ​runs.​ ​It​ ​is​ ​different​ ​from​ ​what​ ​I​ ​initially​ ​thought​ ​in​ ​Question​ ​6,​ ​but​ ​I’m​ ​not surprised​ ​since​ ​I​ ​have​ ​very​ ​little​ ​knowledge​ ​about​ ​baseball. 10. The​ ​baseball​ ​researchers​ ​were​ ​successful​ ​in​ ​finding​ ​better​ ​variables​ ​to​ ​predict​ ​the​ ​total number​ ​of​ ​runs​ ​scored.​ ​The​ ​three​ ​new​ ​variables​ ​all​ ​have​ ​strong​ ​linear​ ​relationships​ ​with runs​ ​scored.​ ​For​ ​example,​ ​in​ ​the​ ​graph​ ​predicting​ ​runs​ ​with​ ​OPS​ ​(on-base​ ​plus​ ​slugging), the​ ​data​ ​points​ ​are​ ​very​ ​close​ ​to​ ​the​ ​regression​ ​line,​ ​which​ ​implies​ ​a​ ​strong​ ​linear relationship​.​ ​The​ ​sum​ ​of​ ​squares​ ​is​ ​12840,​ ​which​ ​is​ ​even​ ​lower​ ​than​ ​the​ ​best​ ​predictor​ ​in the​ ​first​ ​table.​ ​Finally,​ ​the​ ​r²​ ​value​ ​is​ ​0.93,​ ​which​ ​means​ ​that​ ​93%​ ​of​ ​the​ ​variance​ ​in runs​ ​is​ ​explained​ ​by​ ​OPS.​​ ​Of​ ​all​ ​the​ ​variables​ ​that​ ​were​ ​analyzed,​ ​OPS​ ​is​ ​the​ ​best predictor​ ​of​ ​runs.​​ ​It​ ​is​ ​defined​ ​as​ ​the​ ​sum​ ​of​ ​a​ ​player’s​ ​on​ ​base​ ​percentage​ ​and​ ​slugging average.​ ​The​ ​calculation​ ​of​ ​on​ ​base​ ​percentage​ ​involves​ ​the​ ​number​ ​of​ ​hits,​ ​and​ ​slugging average​ ​is​ ​the​ ​number​ ​of​ ​total​ ​bases​ ​divided​ ​by​ ​the​ ​number​ ​of​ ​at-bats.​ ​The​ ​result​ ​makes sense​ ​because​ ​both​ ​hits​ ​and​ ​total​ ​bases​ ​are​ ​good​ ​indicators​ ​of​ ​runs​ ​on​ ​their​ ​own. Summary​ ​Question This​ ​lab​ ​covers​ ​many​ ​concepts​ ​from​ ​chapter​ ​4,​ ​including:​ ​scatterplot,​ ​linear​ ​association, regression​ ​line,​ ​correlation​ ​coefficient,​ ​slope,​ ​coefficient​ ​of​ ​determination​ ​(r²)​ ​and​ ​residual​ ​plot. The​ ​concepts​ ​of​ ​sum​ ​of​ ​squares​ ​and​ ​typical​ ​error​ ​are​ ​not​ ​covered​ ​in​ ​the​ ​textbook;​ ​however,​ ​we talked​ ​about​ ​them​ ​during​ ​the​ ​lecture.​ ​We​ ​reviewed​ ​these​ ​concepts​ ​in​ ​discussion​ ​section​ ​in preparation​ ​for​ ​the​ ​midterm​ ​exam,​ ​and​ ​I​ ​also​ ​did​ ​some​ ​practice​ ​problems​ ​about​ ​these​ ​topics​ ​on my​ ​own. ...
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