Question

A Realtor is interested in modeling the selling price of houses based on the square footage, the age of the house, and the style. The data was collected in the two largest cities in Arkansas and is presented in an excel file. We need two indicator variables for the style of the house. I will choose Traditional as the base category lif the house is a rambler lif the house is victorian rambler Oif not Now use Minitab output to answer the following: 1. Plot Y vs. XI and Y vs. X2. Do you see any curvature in these 2 plots? If so what can be suggested about victor 0if not the variables? Which higher order terms, if any, are needed in the model? This question won't appear in the submission link, but you should make the plots and think about what higher order terms might be necessary. 2. S uppose someone wishes to use the regression model Y: βο + β,K1 + β2X2 + β.xl + β.xl + AKX2 + Alrambler + β71victor + ε a) Write Down the prediction equation. b) Find R2 (as a %, 2 decimals) and interpret it. c) Test if the regression model is useful. (F-test d) Calculate 95% confidence intervals for l, and (2 decimals). X2 Irambler Ivictor X1-sq X1*X2 X1 X2 X3 28000 775 37 Traditional 34000 700 49 Traditional 34500 720 54 Traditional 39900 864 37 Rambler 40000 65035 Traditional 41500 780 79 Victorian 42500 900 48 Traditional 53500 816 35 Rambler 57000 1800 17 Victorian 59000 1340 66 Victorian 59500 1800 18 Rambler 62000 1124 34 Traditional 68500 2880 24 Victorian 72500 1480 75 Rambler 70000 1652 94 Victorian 73112 2088 71 Victorian 76780 1700 34 Traditional 77350 1262 78 Rambler 85590 1500 54 Victorian 79900 1200 35 Victorian 48100 650 45 Traditional 0 600625 1369 2867:5 0 490000 2401 34300 0 518400 2916 38880 0 746496 1369 31968 0 422500 1225 22750 1 608400 6241 61620 0 810000 2304 43200 0 665856 1225 28560 1 3240000 289 30600 1 1795600 4356 88440 0 3240000 324 32400 0 0 1263376 1156 38216 1 8294400 576 69120 0 2190400 5625 111000 1 2729104 8836 155288 1 4359744 5041 148248 0 2890000 1156 57800 0 1592644 6084 98436 1 2250000 2916 81000 11440000 1225 42000 0 422500 2025 29250 0 0 0

Answer 1

Scatterplot of Selling vs X1 90000 80000 70000 60000 50000 40000 30000 20000 1000 1500 2000 2500 3000 X1

Scatterplot of Selling vs X2 90000 80000 70000 60000 50000 30000 20000 10 20 30 40 50 60 70 80 90 100 X2

Graph shows that the data is distributed independent without any curvature.

2) Using Excel:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.820985
R Square	0.674016
Adjusted R Square	0.534308
Standard Error	11801.35
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	6	4031480929	671913488.1	4.824476239	0.007212744
Residual	14	1949805195	139271799.6
Total	20	5981286124
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	3439.088	30244.23111	0.11371054	0.911081829	-61428.33623	68306.51192
X1	62.42002	32.17639197	1.939932185	0.072804956	-6.591478554	131.4315154
X2	-94.0395	479.2688606	-0.196214598	0.84726185	-1121.969016	933.8899223
X1^2	-0.01555	0.007485261	-2.077782585	0.056609328	-0.031607032	0.000501543
X1*X2	0.118454	0.305604947	0.387604802	0.704137596	-0.537003475	0.773911364
Rambler	3081.234	7524.897006	0.409471859	0.688389479	-13058.06531	19220.53244
Victorian	3291.8	8165.320837	0.403144039	0.692931624	-14221.07096	20804.6718

Y' = 3439.088 + 62.42002 * Xi-94.0395 * X2-0.01 555 * Xİ +0.118454 * XiX2 +3081.234 Rambler +3291.8 Victorian

b) R-squared value: 0.674016

The proporiton of variance explained by regression equation is 0.674016

c)

ANOVA
	df	SS	MS	F	Significance F
Regression	6	4031480929	671913488.1	4.824476239	0.007212744
Residual	14	1949805195	139271799.6
Total	20	5981286124

Test statistic is significant and can conlude there is atleast one variable good for prediction.

d) The coefficient iterval for $\beta 1 and\beta 2 is \beta 1=62.0435 and \beta 2=_0.98521$