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Part B Two way ANOVA Dental Health The data set ToothGrowth has measurements of tooth growth ( len ) of guinea pigs for different dosages

Part B Two way ANOVA Dental Health
The data set ToothGrowth has measurements of tooth growth (len) of guinea pigs for different dosages of Vitamin C (dose) and two different delivery methods (supp).
To load the data set, ToothGrowth.txt, change to the proper directory, and then execute the following command in R:
Tooth <- read.table("ToothGrowth.txt",header=T)
attach(Tooth)
Tooth contains three vectors: len, supp, and dose, as described in this table:
Column Descriptions of each column Name of each column in R
1 Tooth length len
2 Delivery method (orange juice or ascorbic acid) supp
3 Dosage level (0.5,1, or 2) in milligrams dose
Use the following commands to test whether dose and supp are treated as categorical variables. If the command responds FALSE, use the factor() command to make them categorical:
is.factor(supp)
is.factor(dose)
1. Create a linear model for Tooth growth (len) in terms of the delivery method (supp), and fill in your answers below.
State the null hypothesis:
H0: The delivery method does not affect tooth growth in guinea pigs
Paste a copy of the anova output for this model here:
Paste a copy of the summary output for this model here:
2. Create a linear model for Tooth growth (len) in terms of the dosage level (dose)
State the null hypothesis:
H0: The dose of vitamin C does not affect tooth growth in guinea pigs
Paste a copy of the anova output for this model here:
Paste a copy of the summary output for this model here:
3. Now create a linear model for Tooth growth (len) in terms of both the delivery method (supp) and the dosage level (dose) using the lm() command:
model<-lm(len~supp+dose)
State the overall null hypothesis:
H0:
Paste a copy of the anova output for this model here:
Paste a copy of the summary output for this model here:
4. Use your outputs above to fill in the p-values and R2 values in the table below. (Recall that the overall p-value can be found in the last line of the output from the summary() command.)
Model p-value R2 value
len~supp
len~dose
len~supp+dose
5. Compare the p-values and R2 values in the table above to determine which model best explains the variability in len. Report that model, here.
Model that best explains the variability in len:

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