Question

In: Statistics and Probability

The variables in the file are Price -Average selling price of houses Location -A code to...

The variables in the file are

Price -Average selling price of houses

Location -A code to indicate the location of the house

Condition -A code to indicate the physical condition of the house

Bedrooms Number of bedrooms in the house

Bathrooms Number of bathrooms in the house

Other Rooms Number of other rooms in the house

(a) Run a regression of Price on Location, Condition, Bedrooms, Bathrooms and Other Rooms. Please attach your Excel file.

(b) What variables seem to be important for buyers of houses? Please explain.

(c) Based on your regression results, if you wanted a low selling price on a house you wanted to purchase, what would you look for? Please explain.

(d) Run a regression of Price on Bedroom, Bathrooms and Other Rooms. Please attach your Excel file

(e) Compare your regression results in (i) to the regression results in (ii). Which would you consider to be a better model and why?

Price   Location   Condition   Bedrooms   Bathrooms   Other Rooms
67000   2   2   2   1   2
68000   2   2   3   1   3
68000   2   2   3   1   3
69000   2   3   2   1   3
72000   2   2   4   2   5
75000   3   4   2   1   3
76000   2   3   2   1   2
76900   2   3   3   1   3
77000   2   3   2   3   5
78000   3   2   2   1   2
79000   2   3   3   2   3
80000   2   3   3   1.5   2
80000   2   3   3   1   2
81000   3   3   2   1   3
82000   2   3   3   1.5   3
83000   2   3   3   1   3
84000   2   2   3   1   3
84000   2   3   3   1.5   3
86250   1   4   4   2   3
87000   3   3   3   2   2
89500   3   2   3   2   2
90400   2   4   4   2   4
90500   3   3   3   1.5   3
91000   3   3   3   2   3
91500   3   1   4   2   3
91500   3   1   4   2   3
92500   3   3   3   1.5   4
93500   2   3   3   2   3
93500   2   3   4   2   2
94000   1   2   3   1.5   3
95500   3   3   3   2   2
96000   2   4   3   2   3
96000   2   3   3   2   3
97900   3   4   3   2   3
98000   3   4   3   2   3
98000   2   4   3   2   4
98000   3   4   3   2   3
99000   2   3   4   2   4
99000   3   2   4   2   4
99000   3   3   3   2   3
102000   3   3   4   2   3
102000   2   3   3   1.5   3
102000   3   3   4   2   3
102000   3   4   3   1.5   3
103000   3   3   3   2   3
103000   3   2   3   1.5   2
103500   3   2   3   2   5
103500   3   3   3   2   5
105000   3   3   3   2   5
105000   3   4   3   1.5   3
108000   2   4   3   2   3
112000   3   2   4   2   4
112500   3   4   3   2   4
114900   2   2   5   2   3
115500   3   4   4   2   3
120500   4   5   3   2   4
122000   2   2   3   3   4
125500   3   3   4   2.5   3
127000   2   4   3   2.5   4
128000   4   4   3   2   4
129900   3   4   4   2.5   3
130350   3   3   3   2   4
132350   3   4   3   2   4
133000   3   3   3   2   4
134500   4   3   3   2   3
135500   3   3   3   3   3
135500   4   3   3   3   3
136500   4   4   3   2   4
136500   4   3   3   2   4
137400   3   3   4   2.5   4
137400   4   3   4   2.5   4
137500   4   4   3   2   4
139500   3   4   4   2.5   4
144000   4   3   4   2.5   5
145000   4   3   3   2   3
149000   4   4   3   2   2
155000   4   4   4   2   5
154000   4   2   3   2   4
155500   3   5   3   2.5   3
156500   4   5   3   2   3
163000   4   3   4   2   4
165000   5   4   4   2   2
167000   5   4   4   2   2
168700   3   5   3   2.5   5
169900   4   5   4   2.5   4
169900   4   5   3   2.5   5
169900   4   5   3   2.5   5
176000   4   5   4   2.5   4
179000   4   5   4   2.5   5
179000   4   5   4   2.5   5
179500   4   4   3   2.5   3
179500   5   4   3   2.5   3
187500   4   3   4   2.5   4
203000   4   5   4   3   6
220000   5   5   4   3.5   5
222000   5   4   3   3.5   6
250000   5   4   4   2.5   4
250000   5   5   4   2.5   4
255000   5   5   4   2.5   4
255000   5   5   3   2.5   4

Solutions

Expert Solution

The Regression calculation done in Excel is given below

Regression Statistics
Multiple R 0.9085
R Square 0.8253
Adjusted R Square 0.8161
Standard Error 19116.0451
Observations 100
ANOVA
df SS MS F Significance F
Regression 5 1.62325E+11 3.2465E+10 88.84234686 4.58807E-34
Residual 94 34349778889 365423180
Total 99 1.96675E+11
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -64558.5034 12387.5357 -5.2116 0.0000 -89154.2459 -39962.7608 -89154.2459 -39962.7608
Location   25533.3487 2474.4568 10.3188 0.0000 20620.2568 30446.4406 20620.2568 30446.4406
Condition   10124.5722 2340.8940 4.3251 0.0000 5476.6723 14772.4721 5476.6723 14772.4721
Bedrooms   8842.6631 3572.1941 2.4754 0.0151 1749.9881 15935.3382 1749.9881 15935.3382
Bathrooms   17202.5553 5030.2405 3.4198 0.0009 7214.8949 27190.2157 7214.8949 27190.2157
Other Rooms 3173.6549 2464.2430 1.2879 0.2009 -1719.1573 8066.4671 -1719.1573 8066.4671

a) The regression line is

Price = -64558 + 25533 * Location + 10124 * Condition + 8842 * Bedrooms + 17202 * Bathroom + 3173 * Other Rooms

b) The top two critical factors for buyer are Location and Bathroom

c) If I have to purchase a house with low selling price I will ignore the coefficients which increase the price of the house. The top two critical factors explain above, will be ignored and make the value = 0. So the price of the house will automatically come down. So I will only consider Other Rooms, then Bedrooms and lastly Condition and ignore location and bathroom

d)

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.701814009
R Square 0.492542903
Adjusted R Square 0.476684868
Standard Error 32243.24002
Observations 100
ANOVA
df SS MS F Significance F
Regression 3 9.69E+10 3.23E+10 31.05952 4.03954E-14
Residual 96 9.98E+10 1.04E+09
Total 99 1.97E+11
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept -19468.36015 19564.65 -0.99508 0.3222 -58303.87522 19367.15493 -58303.87522 19367.15493
Bedrooms   9141.840464 5978.095 1.529223 0.129498 -2724.5851 21008.26603 -2724.5851 21008.26603
Bathrooms   45704.33258 7678.179 5.952497 4.31E-08 30463.26841 60945.39675 30463.26841 60945.39675
Other Rooms 6072.784488 4118.138 1.474643 0.143581 -2101.655472 14247.22445 -2101.655472 14247.22445

The new Regression line is

Price = -19648 + 9141 * Bedrooms + 45704 * Bathrooms + 6072 * OtherRooms

e) The Regression line in 1 better, as the R2 value is closer to 1 in regression equation 1 showing a better fit of the data points.

orchestra answered 1 year ago
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