The monthly, seasonally-adjusted Consumer Price Index for four sectors—Energy, Apparel, Education, and Food and Beverages—was recorded from 2014 to 2018. MegaStat was used to perform a two-factor ANOVA, with α = .05. Study the output from that analysis and answer the following questions.a. Calculate the decision rules, including the critical F values, for each main effect and the interaction.b. Is there a significant interaction? Explain your reasoning using the decision rule from part (a) and the MegaStat output.c. Are any main effects significant? Explain your reasoning using the decision rules from part (a) and the MegaStat output.d. If there are significant main effects, what do the Tukey comparison tests tell you about the source of the significance? Interpret the analysis by stating specifically the source of any significance to find Two factor ANOVA Sector Means: EnergyApparelEducationFood JAN212.1124126.2470243.2370238.9554205.1380 FEB211.1676126.7068243.8340239.3318205.2601 MAR210.6942126.6212244.3252239.2382205.2197 APR211.7020126.5204244.9062239.5556205.6711 MAY212.8016126.5404245.5254239.6846206.1380MonthJUN214.9088126.2178246.1208239.7886206.7590 JUL213.4126126.0226246.6620240.0132206.5276 AUG214.0356125.7544247.2474240.1632206.8002 SEP213.1648126.0730247.8464240.2852206.8424 OCT212.2430126.0326248.4504240.2388206.7412 NOV210.5130125.8722249.0602240.1108206.3891 DEC207.2458125.5746249.6152240.3108205.6866 212.0001126.1819246.4025239.8064206.0977 5replications per cell ANOVA table SourceSS dfMSF p-value Month98.30735118.9370320.061.0000 Sector550,927.336783183,642.4455931242.271.94E-125 Interaction382.415493311.5883480.081.0000 Error28,383.08810192147.828584 Total579,791.14772239 Post hoc analysis p-values for pairwise t-tests for Factor 2 ApparelEnergyFoodEducation 126.1819212.0001239.8064246.4025 Apparel126.1819 Energy212.00011.55E-92 Food239.80647.34E-1141.06E-26 Education246.40252.91E-1181.14E-35.0033 Tukey simultaneous comparison t-values (d.f. = 192) ApparelEnergyFoodEducation 126.1819212.0001239.8064246.4025 Apparel126.1819 Energy212.000138.66 Food239.806451.1912.53 Education246.402554.1615.502.97 critical values for experimentwise error rate: 0.052.60 0.013.18

Month Energy Apparel Education Food Mean JAN 212.1124 126.247 243.237 238.9554 205.138 FEB…

Answered: The monthly, seasonally-adjusted…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The monthly, seasonally-adjusted Consumer Price Index for four sectors—Energy, Apparel, Education, and Food and Beverages—was recorded from 2014 to 2018. MegaStat was used to perform a two-factor ANOVA, with α = .05. Study the output from that analysis and answer the following questions.

a. Calculate the decision rules, including the critical F values, for each main effect and the interaction.

b. Is there a significant interaction? Explain your reasoning using the decision rule from part (a) and the MegaStat output.

c. Are any main effects significant? Explain your reasoning using the decision rules from part (a) and the MegaStat output.

d. If there are significant main effects, what do the Tukey comparison tests tell you about the source of the significance? Interpret the analysis by stating specifically the source of any significance to find

Two factor ANOVA
				Sector
	Means:
		Energy	Apparel	Education	Food
	JAN	212.1124	126.2470	243.2370	238.9554	205.1380
	FEB	211.1676	126.7068	243.8340	239.3318	205.2601
	MAR	210.6942	126.6212	244.3252	239.2382	205.2197
	APR	211.7020	126.5204	244.9062	239.5556	205.6711
	MAY	212.8016	126.5404	245.5254	239.6846	206.1380
Month	JUN	214.9088	126.2178	246.1208	239.7886	206.7590
	JUL	213.4126	126.0226	246.6620	240.0132	206.5276
	AUG	214.0356	125.7544	247.2474	240.1632	206.8002
	SEP	213.1648	126.0730	247.8464	240.2852	206.8424
	OCT	212.2430	126.0326	248.4504	240.2388	206.7412
	NOV	210.5130	125.8722	249.0602	240.1108	206.3891
	DEC	207.2458	125.5746	249.6152	240.3108	205.6866
		212.0001	126.1819	246.4025	239.8064	206.0977

	5	replications per cell

ANOVA table
Source	SS	df	MS	F	p-value
Month	98.30735	11	8.937032	0.06	1.0000
Sector	550,927.33678	3	183,642.445593	1242.27	1.94E-125
Interaction	382.41549	33	11.588348	0.08	1.0000
Error	28,383.08810	192	147.828584
Total	579,791.14772	239

Post hoc analysis
p-values for pairwise t-tests for Factor 2
		Apparel	Energy	Food	Education
		126.1819	212.0001	239.8064	246.4025
Apparel	126.1819
Energy	212.0001	1.55E-92
Food	239.8064	7.34E-114	1.06E-26
Education	246.4025	2.91E-118	1.14E-35	.0033


Tukey simultaneous comparison t-values (d.f. = 192)
		Apparel	Energy	Food	Education
		126.1819	212.0001	239.8064	246.4025
Apparel	126.1819
Energy	212.0001	38.66
Food	239.8064	51.19	12.53
Education	246.4025	54.16	15.50	2.97

critical values for experimentwise error rate:
		0.05	2.60
		0.01	3.18