Question

Can someone please provide a step by step of how I would calcuate a multiple regression anaylsis of the data set attached. How would I properply describe the statistical significance of the independent varibles as well as explaining in the right terms the results?

Assessed Value Heating Area Age 1844002000 177400 1 57001450 185900 1760 179100 1930 170400 1200 1758001550 185900 1785001590 79200 15 186700 1900 79300 1390 174500 183800 176800 1590 3.42 11.50 8.33 0.00 7.42 32.00 16.00 2.00 1.75 2.75 0.00 0.00 12.58 2.75 7.17 1710 1930 1540 1890

Answer 1

here dependent variable = Assessed value

independent variables are Heating are and Age

data

y	Heating Area	Age
184400	2000	3.42
177400	1710	11.5
175700	1450	8.33
185900	1760	0
179100	1930	7.42
170400	1200	32
175800	1550	16
185900	1930	2
178500	1590	1.75
179500	1500	2.75
186700	1900	0
179300	1390	0
174500	1540	12.58
183800	1890	2.75
176800	1590	7.17

data -> data analysis -> regression

Excel result

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.908837453
R Square	0.825985516
Adjusted R Square	0.796983102
Standard Error	2170.933043
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	2	268448596.7	134224298.3	28.47988849	2.77659E-05
Residual	12	56555403.32	4712950.276
Total	14	325004000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	164044.4213	5414.075041	30.29962091	1.04648E-12	152248.1652
Heating Area	10.59019947	3.018174773	3.508809218	0.00431135	4.014161549
Age	-287.7309599	83.70506677	-3.437437792	0.004917674	-470.1086333

y^= 164044.4213 + 10.5902 * Heating Area -287.7310 * Age

if p-value < alpha , the variable is significant

p-value of Heating Area = 0.00431 < 0.05

hence Heating Area is significant

p-value of Age = 0.0049 < 0.05

hence Age is significant