The PLANTS1 data set in the Data Appendix gives the percent of nitrogen in four

Question

The PLANTS1 data set in the Data Appendix gives the percent of nitrogen in four different species of plants grown in a laboratory. The species are Leucaena leucocephala, Acacia saligna, Prosopis juliflora, and Eucalyptus citriodora. The researchers who collected these data were interested in commercially growing these plants in parts of the country of Jordan where there is very little rainfall. To examine the effect of water, they varied the amount per day from 50 millimeters (mm) to 650 mm in 100 mm increments. There were nine plants per species-by-water combination. Because the plants are to be used primarily for animal food, with some parts that can be consumed by people, a high nitrogen content is very desirable.

Run a separate one-way analysis of variance for each species and summarize the results. Since the amount of water is a quantitative factor, we can also analyze these data using regression. Run simple linear regressions separately for each species to predict nitrogen percent from water. Use plots to determine whether or not a line is a good way to approximate this relationship. Summarize the regression results and compare them with the one-way ANOVA results.
DATA

Explanation / Answer

The R program and output is given below:

> tt <- read.csv("clipboard",sep=" ")
> head(tt)
species water pctnit
1       1     1 3.644
2       1     1 3.500
3       1     1 3.509
4       1     1 3.137
5       1     1 3.100
6       1     1 3.081
> tt$species <- as.factor(tt$species)
> tt$water <- as.factor(tt$water)
> nitrogen_lm <- lm(pctnit~.,tt)
> summary(nitrogen_lm)

Call:
lm(formula = pctnit ~ ., data = tt)

Residuals:
     Min       1Q   Median       3Q      Max
-0.59202 -0.15119 -0.00383 0.13816 0.61490

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept) 3.17610    0.04899 64.832 < 2e-16 ***
species2    -0.94697    0.04382 -21.612 < 2e-16 ***
species3     0.24456    0.04382   5.581 6.39e-08 ***
species4    -1.84422    0.04382 -42.089 < 2e-16 ***
water2      -0.22156    0.05797 -3.822 0.000168 ***
water3      -0.23419    0.05797 -4.040 7.17e-05 ***
water4      -0.27592    0.05797 -4.760 3.33e-06 ***
water5      -0.12397    0.05797 -2.139 0.033459 *
water6      -0.07756    0.05797 -1.338 0.182164   
water7      -0.02086    0.05797 -0.360 0.719244   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.2459 on 242 degrees of freedom
Multiple R-squared: 0.9228,    Adjusted R-squared: 0.9199
F-statistic: 321.5 on 9 and 242 DF, p-value: < 2.2e-16

> plot(residuals(nitrogen_lm))

Since there are no outliers, we don't have to run the one-way analysis sepeartely

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