92 7 chla season size speed n 0 2 a1

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Unformatted text preview: ) a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 oPO4 + β7 PO4 + β8 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) Residual standard error: 17.65 on 182 degrees of freedom Multiple R-squared: 0.3731,! Adjusted R-squared: 0.3215 F-statistic: 7.223 on 15 and 182 DF, p-value: 2.444e-12 Model explains less than 50% of the variation in a1, not good! Statistics 503, Spring 2013, ISU 21 21 a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 PO4 + =9.#9>(&39+%" β7 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 oPO4 + β7 PO4 + β8 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) Residual standard error: 17.65 on 182 degrees of freedom Multiple R-squared: 0.3731,! Adjusted R-squared: 0.3215 F-statistic: 7.223 on 15 and 182 DF, p-value: 2.444e-12 Statistics 503, Spring 2013, ISU 21 21 =9.#9>(&39+%" b(c%"(<"*42#I(+$)2<$3*."#0";+(";+%) > algae.torgo.diag <- data.frame(algae.torgo, dffits=dffits(lm.a1, lm.influence(lm.a1)), dfbeta=dfbeta(lm.a1, lm.influence(lm.a1)), CooksD=cooks.distance(lm.a1), hat=lm.influence(lm.a1)$hat) > ggobi(algae.torgo.diag) Statistics 503, Spring 2013, ISU 22 22 =9.#9>(&39+%" b(c%"(<"*42#I(+$)2<$3*."#0";+(";+%) Statistics 503, Spring 2013, ISU 23 23 =9.#9>(&39+%" O+)*I++4*;*+%).2"&$*5#$2<#..6*4")"&'2("*)7"* '+4".: b/*6+%*#&"*I+2(I*)+*<7"<\*/+&*(+&'#.2)6*+/* )7"*"C-.#(#)+&6*0#&2#5."$3*6+%*'2I7)*#$* ,"..*)&6*)+*dC*)7"': O+&'#.2)6*+/*)7"$"*0#&2#5."$*2)$"./*2$*(+)*$+* 2'-+&)#()*#$*#*I++4*$-&"#4942$)&25%)2+(*+/* 0#.%"$: Statistics 503, Spring 2013, ISU 24 24 =.$2(?9.3%+&+$)$&39+%" mxPH mnO2 Cl NO3 4 3 2 1 0 a1 6 7 8 NH4 9 0 50 100 oPO4 150 1 2 3 4 0.5 1.0 PO4 1.5 Chla 2.0 2.0 2.5 2.5 4 3 2 1 0 1 2 3 4 1 2 3 4 50 Chemical 10 20 1.0 1.5 Statistics 503, Spring 2013, ISU 3.0 25 25 a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 PO4 + @/2%$.&.%#.%((/92 β7 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 oPO4 + β7 PO4 + β8 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) > lm.a1 <- lm(a1 ~ .,data=algaet.imp[,c(1:8,9:12)]) > summary(lm.a1) ... Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.934194 1.455774 3.389 0.000859 *** seasonspring -0.195289 0.246673 -0.792 0.429572 seasonsummer -0.083705 0.234152 -0.357 0.721147 seasonwinter -0.174294 0.223544 -0.780 0.436589 sizemedium 0.433500 0.214213 2.024 0.044464 * sizesmall 0.635262 0.241160 2.634 0.009160 ** speedlow 0.465385 0.269474 1.727 0.085862 . ... Statistics 503, Spring 2013, ISU 26 26 a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 PO4 + @/2%$.&.%#.%((/92 β7 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 oPO4 + β7 PO4 + β8 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) > lm.a1 <- lm(a1 ~ .,data=algaet.imp[,c(1:8,9:12)]) > summary(lm.a1) ... Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.934194 1.455774 3.389 0.000859 *** seasonspring -0.195289 0.246673 -0.792 0.429572 seasonsummer -0.083705 0.234152 -0.357 0.721147 seasonwinter -0.174294 0.223544 -0.780 0.436589 sizemedium 0.433500 0.214213 2.024 0.044464 * sizesmall 0.635262 0.241160 2.634 0.009160 ** speedlow 0.465385 0.269474 1.727 0.085862 . ... Statistics 503, Spring 2013, ISU 26 26 a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 PO4 + @/2%$.&.%#.%((/92 β7 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 oPO4 + β7 PO4 + β8 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) > lm.a1 <- lm(a1 ~ .,data=algaet.imp[,c(1:8,9:12)]) > summary(lm.a1) ... Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.934194 1.455774 3.389 0.000859 *** seasonspring -0.195289 0.246673 -0.792 0.429572 seasonsummer -0.083705 0.234152 -0.357 0.721147 seasonwinter -0.174294 0.223544 -0.780 0.436589 sizemedium 0.433500 0.214213 2.024 0.044464 * sizesmall 0.635262 0.241160 2.634 0.009160 ** speedlow 0.465385 0.269474 1.727 0.085862 . ... Statistics 503, Spring 2013, ISU 26 26 a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 PO4 + @/2%$.&.%#.%((/92 β7 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) a1 = β0 + β1 mxPH + β2 mnO2 + β3 Cl + β4 NO3 + β5 NH4 + β6 oPO4 + β7 PO4 + β8 Chla + τseason + τsize + τspeed + ε, ε ∼ N (0, σ 2 ) > lm.a1 <- lm(a1 ~ .,data=algaet.imp[,c(1:8,9:12)]) > summary(lm.a1) ... Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.934...
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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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