Question

a) What is the p-value for the test for βSq. Ft?What is the p-value for the test for βBedrooms?

b) Are these significant? Why or why not?Kindly explain

c) Are Sq. Ft. and Bedrooms highly correlated?How does one know that? Please justify

d) What should we do? ( They are dropping bedrooms here but why)? How do we know which one to leave out in the model?

e) What is the final proposed model?

Obs.	Age	Price ($K)	Sq. Ft	Bedrooms
1	21	240	1185	3
2	22	359	2400	4
3	1	219.9	1450	3
4	25	239.9	1308	3
5	20	259.9	1688	4
6	13	519	2944	5
7	9	614	3721	4
8	29	289	2050	3
9	18	259.9	1504	3
10	12	449.9	2877	4
11	4	735	3992	5
12	11	725	3750	5
13	13	394.9	2889	5
14	17	349.9	1960	3
15	8	525	2625	3
16	10	429	2437	4
17	6	620	3190	4
18	20	329.9	1898	3
19	25	319.5	1757	3
20	5	375	1800	3
21	15	390	2544	4

Answer 1

Solution:

Obs.	Age	Price ($K)	Sq. Ft	Bedrooms
1	21	240	1185	3
2	22	359	2400	4
3	1	219.9	1450	3
4	25	239.9	1308	3
5	20	259.9	1688	4
6	13	519	2944	5
7	9	614	3721	4
8	29	289	2050	3
9	18	259.9	1504	3
10	12	449.9	2877	4
11	4	735	3992	5
12	11	725	3750	5
13	13	394.9	2889	5
14	17	349.9	1960	3
15	8	525	2625	3
16	10	429	2437	4
17	6	620	3190	4
18	20	329.9	1898	3
19	25	319.5	1757	3
20	5	375	1800	3
21	15	390	2544	4

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.955019
R Square	0.912061
Adjusted R Square	0.90229
Standard Error	49.12255
Observations	21
ANOVA
	df	SS	MS	F	Significance F
Regression	2	450481.8	225240.9	93.34379	3.15E-10
Residual	18	43434.45	2413.025
Total	20	493916.2
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	51.03018	55.51726	0.919177	0.370157	-65.6073	167.6676	-65.6073	167.6676
Sq. Ft	0.205729	0.02172	9.471812	2.04E-08	0.160096	0.251361	0.160096	0.251361
Bedrooms	-34.7178	22.99898	-1.50954	0.148516	-83.0369	13.60126	-83.0369	13.60126

Now,

(a)->

p-value for the test for βSq. Ft = 0.0000000204 which is equivalent to zero.

p-value for the test for βBedrooms = 0.1485

(b)->

Here the p-value from the above ANOVA table for significance is almost zero. Hence the given model is significance.

(c)->

	Price ($K)	Sq. Ft	Bedrooms
Price ($K)	1
Sq. Ft	0.949173	1
Bedrooms	0.688301	0.792896	1

Correlation between the Sq.Ft and bedroom is 0.792896, we can't say that Sq. Ft. and Bedrooms are highly correlated.

(d)->

The p-value corresponding to test of significance of regression coefficient Bedroom is very high, So we cannot say that bedroom and Price have significant relationship. Therefore we are dropping the Bedroom.

So, if the p-value of any regression coefficient of a variable is greater than 5%, we drop that variable at 5% level of significance.

(e)->

Hence the final purposed model is:

Price ($K) = 51.03018 + 0.205729 * Sq. Ft