Question

This problem is going to use the data set in R called "ChickWeight" that has 4 variables, as described below.

ChickWeight:
A data frame with 578 observations on 4 variables.
1) weight: a numeric vector giving the body weight of the chick (gm).
2) Time: a numeric vector giving the number of days since birth when the measurement was made.
3) Chick: an ordered factor with levels 18 < ... < 48 giving a unique identifier for the chick. The ordering of the levels groups chicks on the same diet together and orders them according to their final weight (lightest to heaviest) within diet.
4) Diet: a factor with levels 1, ..., 4 indicating which experimental diet the chick received.

Using a significance level of 0.05, is there evidence to support that the weight can be determined by the Time, Diet, and the interaction between the two? (Appears as Time:Diet in RStudio)

Fill in the R code below.

dat.aov = aov( ~ factor( ) *  , data= )
summary( )

Fill in the ANOVA table below.
Type the values into the table EXACTLY as they appear in your output in RStudio.

	df	SS	MS	F	Pr(>F)
factor(Time)					2e-16
Diet					2e-16
factor(Time):Diet					0.00017
Residuals

Is there evidence to support a significant interaction between Time and Diet?
1. ?0:H0: No AB interaction vs ??:Ha: Factors A and B interact
2. ?=0.05α=0.05
3. F =  
4. ??Fα =  
5. Conclusion:
Reject H0
Fail to reject H0
Interpretation:
There is sufficient evidence to support that the interaction between Time and Diet is significant.
There is not sufficient evidence to support that the interaction between Time and Diet is significant.

Answer 1

R code:

dat.aov = aov(lm(weight~ factor(Time)+Diet+factor(Time):Diet, data=ChickWeight))
summary(dat.aov)

Output:

summary(dat.aov)
                   Df Sum Sq Mean Sq F value   Pr(>F)  
factor(Time)       11 2067050 187914 157.808 < 2e-16 ***
Diet                   3 129721   43240 36.313 < 2e-16 ***
factor(Time):Diet 33   86676    2627   2.206 0.000172 ***
Residuals         530 631110    1191                   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

	df	SS	MS	F	Pr(>F)
factor(Time)	11	2067050	187914	157.808	2e-16
Diet	3	129721	43240	36.313	2e-16
factor(Time):Diet	33	86676	2627	2.206	0.00017
Residuals	530	631110	1191

3. F = 2.206

4. Fα = F_0.05,33,530=1.4585

5. Conclusion:
Reject H0

(since F>Fα)

Interpretation:

There is sufficient evidence to support that the interaction between Time and Diet is significant.