Question

1) Run a regression model to estimate the cost of a building using average storey height (mean centered) and total floor area (mean centered)

2) Run a regression model to estimate the cost of a building using average storey height (mean centered), total floor area (mean centered), and the type of construction (dummy coded with reinforced concrete as the control group)

Interpret the slopes, intercepts, and regression statistics in the models

Building type	Average floor area (m2)	Total floor area (m2)	avg story height(cms)	COST (HK$)
1	1852	81478	410	1467000000
1	1608	64313	411	1150000000
1	1430	55783	403	1028000000
1	1562	57794	390	1100000000
1	1109	37695	391	728000000
1	905	28048	382	558000000
1	1852	81478	410	1467000000
1	901	30617	391	631000000
1	1727	69062	400	1223000000
1	1161	37148	394	761000000
1	1004	37141	400	713000000
1	1216	38912	390	784000000
1	2007	88302	422	1593000000
1	2983	173000	440	2649000000
2	1523	70080	372	1210000000
2	912	28286	370	607000000
2	1343	53715	382	977000000
2	1175	32908	381	700000000
2	1203	40902	393	811000000
2	1393	52951	392	1001000000
2	713	20681	375	468000000
2	1047	37681	411	747000000
2	1506	63270	421	1156000000
2	1642	70624	423	1268000000
2	1848	73936	403	1333000000
2	1627	60190	402	1162000000
2	1301	40321	384	864000000
2	905	25330	405	561000000
2	1727	72514	400	1303000000
2	1414	52318	392	1013000000
2	2001	76022	431	1487000000
2	400	9200	380	263000000
2	3100	102190	454	2112000000
2	1677	83860	410	1519000000
2	2415	130032	420	2045000000
2	1555	46637	410	1025000000
2	792	20596	420	540000000
Building Type
1	Reinforced Concrete
2	Steel

Answer 1

At first I use regression analysis in excel to show the cost of the building depending upon avg storey of building & total floor cost of two type of building.

So y = alpha + beta1 total floor area + beta2 avg storey building + error

Please look at the SPSS output below :-

In the above output model summary table shows the R-square value. That defines goodness of the fit of the model. Higher the value of R^2 higher is the goodness of fit. Here Rsquare = .98 means 98% of the model is defined by the two independent variables and rest 2% by the error.

Now our null hypothesis is H0 : alpha = 0 = beta

alternative Ha : alpha 0 beta

By seeing the p-value at co-efficient table we can say that p value for the constant that is alpha and avg. storey building that beta1 are less than 0.05 at 95% confidence interval & also less than 0.05 in case of total floor area that coefficient of total floor area beta2. so null hypothesis is rejected in case of constant & beta1 beta2. This model is good & significancde to the test. We can have better rsquare value also.So, we perform an another model where we only consider the building type 1.

Please look at the below output of SPSS :-

Here R square is .992. That is 99.2% of the model is derived by the two independent variable. Now p value of alpha , beta1 are greater than 0.05 & less than 0.05 for beta2. so we cannot reject null hypothesis for alpha & beta1 , which is a contradictory result. But here Rsquare value is more so we could have better fit of the model in this case but all the parameters are not significant to the test.