The experiment for Spruce Moth Traps is conducted using 5 re

The experiment for Spruce Moth Traps is conducted using 5 replicates. Response is the number of spruce moths found in trap after 48 hours. Factor 1 is the Location of trap in tree (top branches, middle branches, lower branches, ground) and Factor 2 is the Type of lure in trap (scent, sugar, chemical)

(a) Conduct an ANOVA (significant level 0.05). What are your conclusions?

(b) Analyze the residuals and comment on model adequacy.

(c) Draw main effects plot and interaction plots and interpreter the plots

Location

Scent

Sugar

Chemical

Top

28

35

32

19

22

29

32

33

16

15

21

18

13

17

20

Middle

39

36

37

12

38

40

42

44

18

25

27

28

21

22

36

Lower

44

42

35

21

17

39

38

31

41

32

29

31

29

37

34

Ground

17

18

22

12

27

25

23

15

14

19

29

16

14

16

19

Question 2. (60 points) The data (X1, X2, X3, X4, X5, X6, X7) for each city are collected.

Y = total overall reported crime rate per 1 million residents

X1 = reported violent crime rate per 100,000 residents

X2 = annual police funding in $/resident

X3 = % of people 25 years+ with 4 yrs. of high school

X4 = % of 16 to 19 year-olds not in highschool and not highschool graduates.

X5 = % of 18 to 24 year-olds in college

X6 = % of people 25 years+ with at least 4 years of college

Location	Scent	Sugar	Chemical
Top	28	35	32
	19	22	29
	32	33	16
	15	21	18
	13	17	20
Middle	39	36	37
	12	38	40
	42	44	18
	25	27	28
	21	22	36
Lower	44	42	35
	21	17	39
	38	31	41
	32	29	31
	29	37	34
Ground	17	18	22
	12	27	25
	23	15	14
	19	29	16
	14	16	19

Solution

2 Sol)

The data (X1, X2, X3, X4, X5, X6, X7) for each city are collected.

Y = total overall reported crime rate per 1 million residents

X1 = reported violent crime rate per 100,000 residents

X2 = annual police funding in $/resident

X3 = % of people 25 years+ with 4 yrs. of high school

X4 = % of 16 to 19 year-olds not in highschool and not highschool graduates.

X5 = % of 18 to 24 year-olds in college

X6 = % of people 25 years+ with at least 4 years of college

The Regression Model is y=b0+b1 X1+ b2 X2 + b3 X3+ b4 X4+b5 X5+b6 X6

Using Excel

Hence The fitted Regression is

y=100.39+0.332 X1 +3.998 X2 +1.85 X3+ 7.83 X4 + 2.558 X5 - 3.23 X6

1Sol)

a) The \'null hypothesis: H0: There is no difference in means of factor1 and factor 2

\'Alternative hypothesis\' H1: There is a difference in meansfactor1 and factor 2

From SPSSwe have

a. R Squared = .421 (Adjusted R Squared = .289)

Hence p value=0.003 and alpha=0.04

Hence there is no significant difference betwen factor 1 and factor 2

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.783046
R Square	0.613161
Adjusted R Square	0.559183
Standard Error	195.1578
Observations	50
ANOVA
	df	SS	MS	F	Significance F
Regression	6	2595877	432646.2	11.35954	1.42E-07
Residual	43	1637723	38086.58
Total	49	4233600
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	100.3936	370.6932	0.270827	0.78782	-647.18	847.9676	-647.18	847.9676
X1	0.332336	0.059617	5.574486	1.52E-06	0.212106	0.452566	0.212106	0.452566
X2	3.998174	2.682483	1.490475	0.143399	-1.41157	9.407915	-1.41157	9.407915
X3	1.857912	5.240873	0.354504	0.724694	-8.71131	12.42714	-8.71131	12.42714
X4	7.838861	7.759872	1.010179	0.31806	-7.81041	23.48813	-7.81041	23.48813
X5	2.558769	3.426952	0.74666	0.459332	-4.35234	9.469876	-4.35234	9.469876
X6	-3.23116	10.71537	-0.30154	0.764453	-24.8408	18.37844	-24.8408	18.37844