75 100 52 predicted values 4 y 3 2 1 0 000 025 050 x

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Unformatted text preview: ;I+&6*<+'52(#)2+(3*"I ￿ a1 ￿ a1 = = 4.38 − 1.18Cl + 0.34oPO4 − 0.53Chla 1 if size=“large” and speed=“high” 4.38 − 4.06 − (6.34 − 1.67)Cl + 0.34oPO4 − 0.53Chla if size=“large” and speed=“low” Statistics 503, Spring 2013, ISU 38 38 592'"*(/92( S7"*2'-+&)#()*0#&2#5."$*/+&*-&"42<)2(I*#.I#"* )6-"*?*#&"8 =7.+&24"$3*+&)7+J7+$-7#)"*#(4*=7.+&+-76.. a2)7*42Q"&2(I*#'+%()$*56*$2E"*#(4*$-""4*+/* )7"*&20"& S7"*'+4".*"C-.#2(*#.'+$)*fWg*+/*)7"*#.I#"* <+%()$: J.%$*$)#)"'"()$*#5+%)*)&#($/+&'#)2+($*#(4* 2'-%)#)2+($: Statistics 503, Spring 2013, ISU 39 39 F2)%.4.%)$)/92 a7"(*=7.+&24"$*#&"*72I73*#.I#"*2$*.+,"&3* "C<"-)*2/*)7"*&20"&*2$*.#&I"*#(4*$.+,: a7"(*=7.+&+-76..*2$*72I73*#.I#"*2$*.+,"&3*/+&* #..*&20"&*<+(42)2+($ a7"(*+JLP*2$*72I73*#.I#"*2$*.+,"&3*"C<"-)*2/** 2)*2$*#*.#&I"*&20"&*)7"(*)7"&"*2$*(+*&".#)2+($72-: Statistics 503, Spring 2013, ISU 40 40 F2)%.4.%)$)/92 a7"(*=7.+&24"$*#&"*72I73*#.I#"*2$*.+,"&3* "C<"-)*2/*)7"*&20"&*2$*.#&I"*#(4*$.+,: a7"(*=7.+&+-76..*2$*72I73*#.I#"*2$*.+,"&3*/+&* #..*&20"&*<+(42)2+($ a7"(*+JLP*2$*72I73*#.I#"*2$*.+,"&3*"C<"-)*2/** 2)*2$*#*.#&I"*&20"&*)7"(*)7"&"*2$*(+*&".#)2+($72-: Remember a1 was log’d so need to raise predicted values to exp to convert back to counts, similarly for the explanatory variable values. Statistics 503, Spring 2013, ISU 40 40 F2)%.4.%)$)/92 a7"(*=7.+&24"$*#&"*72I73*#.I#"*2$*.+,"&3* "C<"-)*2/*)7"*&20"&*2$*.#&I"*#(4*$.+,: a7"(*=7.+&+-76..*2$*72I73*#.I#"*2$*.+,"&3*/+&* #..*&20"&*<+(42)2+($ a7"(*+JLP*2$*72I73*#.I#"*2$*.+,"&3*"C<"-)*2/** 2)*2$*#*.#&I"*&20"&*)7"(*)7"&"*2$*(+*&".#)2+($72-: Statistics 503, Spring 2013, ISU 40 40 =:%2 ["-"#)*#I#2(*/+&*#M;#H` Statistics 503, Spring 2013, ISU 41 41 F2)%.4.%)$)/92 !+4".*$%''#&68 > summary(lm5.a1) Coefficients: (Intercept) sizemedium sizesmall Cl speedlow speedmedium Chla oPO4 sizemedium:Cl sizesmall:Cl Cl:speedlow Cl:speedmedium sizemedium:oPO4 sizesmall:oPO4 Found something wrong in the coefficients reported on previous slides! Estimate Std. Error t value Pr(>|t|) 4.4166 0.7587 5.822 2.51e-08 *** 1.7956 0.8078 2.223 0.027432 * 1.1755 0.8004 1.469 0.143614 -1.2126 0.4543 -2.669 0.008271 ** -4.0583 1.4860 -2.731 0.006923 ** 0.4537 0.6810 0.666 0.506093 -0.5211 0.1599 -3.259 0.001330 ** 0.3249 0.3251 0.999 0.318875 0.9302 0.4226 2.201 0.028960 * 0.9778 0.4985 1.961 0.051316 . 1.6818 0.5737 2.932 0.003795 ** -0.1889 0.2959 -0.639 0.523871 -1.3798 0.3810 -3.621 0.000378 *** -1.1083 0.3650 -3.037 0.002735 ** Statistics 503, Spring 2013, ISU 42 42 β8 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ ) a1 = β0 + β1 Cl + β2 oPO4 + β3 Chla + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) ￿ a1 = = = = ... ￿ a1 ￿ a1 = ￿ a1 ￿ a1 = ￿ a1 = = ￿ a1 ￿ a1 = ￿ a1 ￿ a1 = = = = F2)%.4.%)$)/92 5.27 − 0.41Cl − 0.69oPO4 − 0.55Chla if size=“large” and speed=“high” 5.77 − 0.41Cl − 0.69oPO4 − 0.55Chla if size=“small’ and speed=“high” 5.57 − 0.41Cl − 0.69oPO4 − 0.55Chla if size=“medium” and speed=“high” 5.76 − 0.41Cl − 0.69oPO4 − 0.55Chla if size=“lareg” and speed=“low” !+4".8 4.42 − 1.21Cl + 0.32oPO4 − 0.52Chla if size=“large” & speed=“high” 4.42 + 0.45 + (−1.21 − 0.19)Cl + 0.32oPO4 − 0.52Chla if size=“large” & speed=“medium” 4.42 − 4.06 + (−1.21 + 1.68)Cl + 0.32oPO4 − 0.52Chla if size=“large” & speed=“low” 4.42 + 1.80 + (−1.21 + 0.93)Cl + (0.32 − 1.38)oPO4 − 0.52Chla if size=“medium” & speed=“high” 4.42 + 1.80 + 0.46 + (−1.21 + 0.93 − 0.19)Cl + (0.32 − 1.38)oPO4 − 0.52Chla if size=“medium” & speed=“medium” 4.42 + 1.80 − 4.06 + (−1.21 + 0.93 + 1.68)Cl + (0.32 − 1.38)oPO4 − 0.52Chla if size=“medium” & speed=“low” 4.42 + 1.18 + (−1.21 + 0.98)Cl + (0.32 − 1.11)oPO4 − 0.52Chla if size=“small” & speed=“high” 4.42 + 1.18 + 0.46 + (−1.21 + 0.98 − 0.19)Cl + (0.32 − 1.11)oPO4 − 0.52Chla if size=“small” & speed=“medium” 4.42 + 1.18 − 4.06 + (−1.21 + 0.98 + 1.68)Cl + (0.32 − 1.11)oPO4 − 0.52Chla if size=“small” & speed=“low” For Cl = ￿ a1 = 4.38 − 1.18Cl + 0.34oPO4 − 0.53Chla if size=“l...
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This note was uploaded on 02/06/2014 for the course STAT 503 taught by Professor Staff during the Fall '08 term at Iowa State.

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