date	house	gdp	interest
5/15/2002	6.87309	3.567727	5.515236
8/15/2002	4.109163	0.978795	4.995225
11/15/2002	2.961117	5.423882	4.869358
2/15/2003	0.001663	-8.33886	3.949507
5/15/2003	4.458599	3.519417	5.059033
8/15/2003	4.363868	1.757381	4.787134
11/15/2003	3.559352	7.508813	5.241011
2/15/2004	-1.77336	-7.64669	4.698297
5/15/2004	-4.21497	3.802526	5.370114
8/15/2004	-0.957	1.335485	5.198758
11/15/2004	-0.27107	5.777947	4.602777
2/15/2005	-2.84392	-7.55266	4.731204
5/15/2005	-1.9248	4.582637	4.691053
8/15/2005	-2.66549	1.452142	4.22991
11/15/2005	0.383516	6.3435	4.91435
2/15/2006	-1.81332	-8.43442	4.436944
5/15/2006	0.195047	3.106712	4.032395
8/15/2006	-0.8101	2.291104	4.805018
11/15/2006	0.599602	6.679772	5.76904
2/15/2007	-0.24096	-6.4464	5.8079
5/15/2007	2.594526	3.831032	4.741592
8/15/2007	1.75771	0.734607	5.338449
11/15/2007	1.477653	5.654151	5.229798
2/15/2008	-1.90113	-8.40132	4.805332
5/15/2008	-2.77744	5.124434	4.931121
8/15/2008	-3.46076	1.81273	4.757427
11/15/2008	-1.29487	4.589894	5.114191
2/15/2009	-1.75335	-9.12946	4.113942
5/15/2009	4.466014	2.094695	4.591901
8/15/2009	3.47313	-0.78079	4.47945
11/15/2009	5.028565	5.666131	4.930284
2/15/2010	2.351384	-7.38068	4.597266
5/15/2010	2.069748	7.19547	4.903915
8/15/2010	-1.0228	0.404348	4.308478
11/15/2010	-0.60982	5.12644	4.924659
2/15/2011	-1.73833	-8.40839	4.076878
5/15/2011	-0.71929	6.170844	4.416935
8/15/2011	-2.5637	0.669862	3.966828
11/15/2011	-1.1988	3.757904	4.0925
2/15/2012	0.708697	-8.26666	3.871466
5/15/2012	1.004013	5.402672	2.876166
8/15/2012	-1.69086	-2.12252	1.661411
11/15/2012	2.281237	3.75929	2.916036
2/15/2013	0.768385	-7.6672	3.07701
5/15/2013	3.337864	4.972977	2.946042
8/15/2013	2.98015	-1.1022	2.701018
11/15/2013	5.336964	4.785339	3.343269
2/15/2014	1.17894	-7.95315	3.562481
5/15/2014	3.460043	3.561437	3.36145
8/15/2014	2.445838	-1.22822	3.002023
11/15/2014	3.413563	4.324454	2.988697
2/15/2015	3.584572	-7.54435	2.353216
5/15/2015	9.109359	3.23635	2.099569
8/15/2015	2.846572	-0.20878	2.305717
11/15/2015	-2.50739	3.377668	2.402963
2/15/2016	-0.39353	-7.16959	2.773669
5/15/2016	2.795689	5.264798	1.947814
8/15/2016	2.20637	-0.74237	1.192518
11/15/2016	5.534279	6.743221	1.950721
2/15/2017	2.469766	-6.73855	2.307955
5/15/2017	1.935996	3.979979	2.322338
8/15/2017	-1.94167	-0.49026	2.014327
11/15/2017	-0.84948	3.682684	2.014967
2/15/2018	-1.83107	-6.28961	2.330636
5/15/2018	-1.59119	5.189821	2.388094
8/15/2018	-2.54714	-0.36878	2.177522
11/15/2018	-4.42172	4.347746	2.068032
2/15/2019	-4.23216	-6.22962	2.12
5/15/2019	-0.80289	5.109959	1.016503
8/15/2019	3.462172	-0.40122	0.574019
11/15/2019	4.477075	2.737958	0.433426
2/15/2020	2.258426	-7.44312	0.662433
5/15/2020	-0.76259	-1.76822	2.783459
8/15/2020	-0.12583	1.587054	-0.68343
11/15/2020	3.077771	7.743045	0.029415
2/15/2021	7.365388	-4.75805	0.756064

The 'house price' data set has three variables:

'house': the growth rate in percentage of real price of houses in Sydney. For example, an observation of 2 would mean that house price has increased by 2% over the time period.

'gdp': the growth rate in percentage of Australian real gdp per capita

'interest': the growth rate in percentage of the real interest rate that is represented by the yield of 10-year Australian government bonds.

REQUIREMENT:Deliver a REPORT answering below questions (analyze and make comment)

IMPORTANT: **PLEASE, INCLUDE EXCEL FULLCALCULATION**

Sydney residents usually ask if they would get higher price by selling their houses in a particular season, or if they would obtain lower price by buying houses in some other seasons. This question uses variable 'house' in data set 'house price' to investigate whether the mean house prices in different quarters are different.

a) Specify the null hypothesis and alternative hypothesis for a test that would provide useful information for Sydney residents in making selling/buying decisions.

b) Use the provided data, create four samples of house price growth rates, each sample for a separate quarter. Conduct the test using one factor ANOVA.

c) Use the provided data, construct a dummy variable for each of the four quarters. Estimate a linear regression of house price growth on dummies (be careful of dummy trap). Use the regression results to conduct the test.