b. Use the ANOVA table to test for the global utility of the model. Clearly stat

Question

b. Use the ANOVA table to test for the global utility of the model. Clearly state all 5 steps

c. Test whether there is a significant interaction. Clearly state all 5 steps.

d. Is it appropriate to test for main effect of factor A or B? Why? If yes, use hypothesis tests to determine which of the factors are significant and clearly state all 5 steps for each test.

please answer all question!

thank you so much!

Suppose you want to determine whether the brand of laundry detergent used and the temperature affects the amount of dirt removed from your laundry. To this end, you buy two different brand of detergent ( Super and Best) and choose three different temperature levels (cold, warm, and hot) Then you divide your laundry randomly into 6r piles of equal size and assign each r-4 piles into the combination of (Super and Best) and (cold,warm, and hot) best 6,6,4,4 super Cold4,5,6,5 Warm7,9,8,1213,15,12,12 Hot 10,12,11,912,13,10,13 (a). Complete the ANOVA table (show work) DF MS Source Detergent (A) Temperature (B) Interaction Error Total 20.167 200.333 16.333 273.833

Explanation / Answer

a)

MS = SS/df

df = r-1

for temprature, df = 3-1 =2

for detergent df = 2-1 =1

df interaction = 2*1 =2

total df = n-1 = 24-1 = 23

df error = 23-2-1-2 = 18

b) since p-value of detergent , temperature and interaction < 0.05

the overall model is significant

c) p-value for interaction = 0.03722 < 0.05

the interaction is significant

ANOVA Source of Variation SS df MS F P-value temperature 200.3333333 2 100.1666667 48.72972973 5.43985E-08 detergent 20.16666667 1 20.16666667 9.810810811 0.00575844 Interaction 16.33333333 2 8.166666667 3.972972973 0.037224336 Error 37 18 2.055555556 Total 273.8333333 23

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