explanatory variables are inorganic phosphorus (inorg) and organic phosphorus or

Question

explanatory variables are inorganic phosphorus (inorg) and organic phosphorus org The R commands for reading in the data and plotting the data are given below: > PAphosc (64,60,71,61,54,77,81,93,93,51,76,96,77,93,95,54,168,99) >inorgc(0.4,0.4,3.1,0.6,4.7,1.7,9.4,10.1,11.6,12.6,10.9,23.1 23.1,21.6,23.1,1.9,26.8,29.9) > org par (mfrow ,2)) > plot(inorg , PAphos.xlab="Înorganic phosphate", ylab="Plant available phosphate > plot(org, PAphos,xlab-"Organic phosphate", ylab-"Plant available phosphate") 0 0 5 10 20 30 20 30 40 50 60 Inorganic phosphate Organic phosphate (a) Fit the three different normal linear models in R to: (i) The plant-available phosphorous linearly regressed on inorganic phosphorous: (ii) The plant-available phosphorous inearly regressed on organic phosphorous; (iii) The plant-available phosphorous linearly regressed on both inorganic and or ganic phosphorous. You should provide both your R commands and the associated R output. This is most easily done by simply cutting and pasting the R commands/output into an editor

Explanation / Answer

> PAphos=c(64,60,71,61,54,77,81,93,93,51,76,96,77,93,95,54,168,99)
> inorg=c(0.4,0.4,3.1,0.6,4.7,1.7,9.4,10.1,11.6,12.6,10.9,23.1,23.1,21.6,
+ 23.1,1.9,26.8,29.9)
> org=c(53,23,19,34,24,65,44,31,29,58,37,46,50,44,56,36,58,51)
> model_1=lm(PAphos~inorg)
> summary(model_1)

Call:
lm(formula = PAphos ~ inorg)

Residuals:
Min 1Q Median 3Q Max
-31.486 -8.282 -1.674 5.623 59.337

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 59.2590 7.4200 7.986 5.67e-07 ***
inorg 1.8434 0.4789 3.849 0.00142 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 20.05 on 16 degrees of freedom
Multiple R-squared: 0.4808, Adjusted R-squared: 0.4484
F-statistic: 14.82 on 1 and 16 DF, p-value: 0.001417

> ## ii)
> model_2=lm(PAphos~org)
> summary(model_2)

Call:
lm(formula = PAphos ~ org)

Residuals:
Min 1Q Median 3Q Max
-41.437 -14.575 -1.646 11.208 75.563

Coefficients:
Estimate Std. Error t value Pr(>|t|)  
(Intercept) 51.7013 20.4469 2.529 0.0224 *
org 0.7023 0.4632 1.516 0.1489  
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 26.02 on 16 degrees of freedom
Multiple R-squared: 0.1256, Adjusted R-squared: 0.071
F-statistic: 2.299 on 1 and 16 DF, p-value: 0.1489

>
> ## iii)
>
> ## ii)
> model_3=lm(PAphos~inorg+org)
> summary(model_3)

Call:
lm(formula = PAphos ~ inorg + org)

Residuals:
Min 1Q Median 3Q Max
-32.828 -8.440 -1.118 6.694 58.757

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 56.25102 16.31074 3.449 0.00358 **
inorg 1.78977 0.55674 3.215 0.00579 **
org 0.08665 0.41494 0.209 0.83740
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 20.68 on 15 degrees of freedom
Multiple R-squared: 0.4823, Adjusted R-squared: 0.4133
F-statistic: 6.988 on 2 and 15 DF, p-value: 0.00717

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