This problem is going to use the data set in R called \"ChickWeight\" that has 4...

Free

70.2K

Verified Solution

Question

Basic Math

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 birthwhen the measurement was made.
3) Chick: an ordered factor with levels 18 < ... < 48 givinga unique identifier for the chick. The ordering of the levelsgroups chicks on the same diet together and orders them accordingto their final weight (lightest to heaviest) within diet.
4) Diet: a factor with levels 1, ..., 4 indicating whichexperimental diet the chick received.

Using a significance level of 0.05, is there evidence to supportthat the weight can be determined by the Time, Diet, and theinteraction 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 youroutput in RStudio.

dfSSMSFPr(>F)
factor(Time)2e-16
Diet2e-16
factor(Time):Diet0.00017
Residuals

Is there evidence to support a significant interaction betweenTime and Diet?
1. ?0:H0: No AB interaction vs ??:Ha: Factors A and Binteract
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 interactionbetween Time and Diet is significant.
There is not sufficient evidence to support that the interactionbetween Time and Diet is significant.

Answer & Explanation Solved by verified expert
4.1 Ratings (555 Votes)

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 = F0.05,33,530=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.


Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students