A researcher wants to understand how an annual mortgage payment (in Ringgit) depends on income level and zonal location allowing for interaction. The data are shown below: SUMMARY LOW MEDIUM HIGH Total KOTA KINABALU Count 5 5 5 15 Sum 799 959 1020 2778 Average 159.8 191.8 204 185.2 Variance 1151.2 40.7 607.5 886.314286 SANDAKAN Count 5 5 5 15 Sum 1197 1333 1971 4501 Average 239.4 266.6 394.2 300.066667 Variance 5108.8 1918.8 8242.2 9241.92381 TAWAU Count 5 5 5 15 Sum 742 915 1068 2725 Average 148.4 183 213.6 181.666667 Variance 3394.8 10957.5 532.8 5012.95238 LAHAD DATU Count 5 5 5 15 Sum 670 651 806 2127 Average 134 130.2 161.2 141.8 Variance 1480 1181.7 1993.7 1534.31429 KENINGAU Count 5 5 5 15 Sum 98 205 237 540 Average 19.6 41 47.4 36 Variance 25.3 37.5 131.3 206.857143 Total Count 25 25 25 Sum 3506 4063 5102 Average 140.24 162.52 204.08 Variance 7042.27333 8172.92667 14964.4933 ANOVA Source of Variation SS df MS F P-value F crit Zonal Location 540452.72 4 135113.18 55.0676207 2.0312E-19 2.5252151 Income 52493.1467 2 26246.5733 10.6972269 0.00010634 3.15041131 Interaction 36644.72 8 4580.59 1.86689554 0.08222561 2.09696831 Within 147215.2 60 2453.58667 Total 776805.787 74 i. Determine the F-Statistics and P-Value for income, zonal location and interaction between income and zonal location.

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Author:Amos Gilat

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A researcher wants to understand how an annual mortgage payment (in Ringgit) depends on income level and zonal location allowing for interaction. The data are shown below:


SUMMARY	LOW	MEDIUM	HIGH	Total
KOTA KINABALU
Count	5	5	5	15
Sum	799	959	1020	2778
Average	159.8	191.8	204	185.2
Variance	1151.2	40.7	607.5	886.314286

SANDAKAN
Count	5	5	5	15
Sum	1197	1333	1971	4501
Average	239.4	266.6	394.2	300.066667
Variance	5108.8	1918.8	8242.2	9241.92381

TAWAU
Count	5	5	5	15
Sum	742	915	1068	2725
Average	148.4	183	213.6	181.666667
Variance	3394.8	10957.5	532.8	5012.95238

LAHAD DATU
Count	5	5	5	15
Sum	670	651	806	2127
Average	134	130.2	161.2	141.8
Variance	1480	1181.7	1993.7	1534.31429

KENINGAU
Count	5	5	5	15
Sum	98	205	237	540
Average	19.6	41	47.4	36
Variance	25.3	37.5	131.3	206.857143

Total
Count	25	25	25
Sum	3506	4063	5102
Average	140.24	162.52	204.08
Variance	7042.27333	8172.92667	14964.4933


ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Zonal Location	540452.72	4	135113.18	55.0676207	2.0312E-19	2.5252151
Income	52493.1467	2	26246.5733	10.6972269	0.00010634	3.15041131
Interaction	36644.72	8	4580.59	1.86689554	0.08222561	2.09696831
Within	147215.2	60	2453.58667

Total	776805.787	74

i. Determine the F-Statistics and P-Value for income, zonal location and interaction between income and zonal location.

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