A developer who specializes in summer cottage properties is considering purchasing a large tract of land adjoining a lake. The current owner of te tract has already subdivided the land into separate building lots and has prepared the lots by removing some of the trees. The developer wants to forecast the value of each lot. From previous experience, she knows that the most important factors affecting price of a lot are lot size, number of mature trees, distance to the lake, and whether approval has been granted for a septic field. From a nearby area, she gathers the relevant data for 60 recently sold lots. The data are shown below and include the price in $1000, the lot size in 1000 sq ft, the number of mature trees, the distance to the lake in meters, and whether approval already been granted for a septic field.
1. Identify the independent variable(s) for these data and for the regression analysis in the problem:
2. Identify the dependent variable(s) for these data and for the regression analysis in the problem:
3. Find the estimated multiple regression equation for determining price based on lot size, number of mature trees, and distance from the lake.
equation:
4. interpret the coefficients from qu. 3 in the spaces below:
coefficient for lot size:
coefficient for number of mature trees:
coefficient for distance to the lake:
5. Estimate the average price for a lot that is 40,000 sq ft in size, has 50 mature trees, and is 50 metres from the lake.
6. Give the name of the measure that would be most appropriate to be used to determine how good a fit is provided by the estimated regression equation; as well, indicate the value of this measure.
		name of measure:
		valye of measure:
7. Explain what the value of the measure from question 6 indicates about how good a fit is provided by the estimated regression equation
8. State the hypothesis used for testing to see if the model is overall significant. Express the hypotheses in symbolic form if possible.
	H0:
	HA:
9. Indicate the p-value that would be used to test the hypotheses in question 8 above:
10. Complete the hypothesis test for the hypotheses in qu. 8 to determine if the model is significant overall (using significance level of 0.05). Give a complete summary and conclusions.
11. State the hypothesis used to test if price is significantly related to the lot size. Express the hypotheses in symbolic form if possible.
	H0:
	HA:
12. Indicate the p-value that would be used to test the hypotheses in question 11 above:
13. Complete the hypothesis test for the hypotheses in qu. 11 to determine if price is significantly related to the lot size (using significance level of 0.05). Give a complete summary and conclusions.
14. The developer believes that septic approval is also important to potential buyers. Find a new regression equation that also includes whether approval has already been granted for a septic field.
equation:
15. What would you estimate the average price to be for a lot of size 50,000 sq ft with 60 mature trees, located 30 meters from the lake and having already received approval for a septic field?
16. State the hypothesis used to test if having a septic approval is significantly related to the price of the lot. Express the hypotheses in symbolic form if possible.
	H0:
	HA:
17. Indicate the p-value that would be used to test the hypotheses in question 16 above:
18. Complete the hypothesis test for the hypotheses in qu. 16 to determine if having a septic approval is significantly related to the price of the lot (using significance level of 0.05). Give a complete summary and conclusions.
Price	Lot size	Trees	Distance	Septic
105.4	41.2	24	42	yes
91.2	44.8	5	71	no
183.3	21.3	72	43	yes
93.8	43.9	58	14	no
207.5	57.7	52	12	yes
130.9	33.4	78	26	no
162.3	31.4	65	51	no
18.8	27.4	22	0	no
80.5	26.2	68	83	no
38.3	40	57	76	no
71.3	47.6	53	35	no
55.5	31.6	36	26	no
85.7	21.6	23	24	no
110.5	36.3	48	98	yes
85.1	47.2	61	59	no
78.3	30.5	41	55	no
27.2	41.8	1	60	no
70.9	20.6	20	33	no
101.4	35.3	38	75	yes
133.3	40.1	68	0	no
117.7	35.6	24	41	no
49.7	20.6	16	77	no
49.6	22.4	32	86	no
83.2	45.8	77	19	no
81.3	29.4	40	0	no
152.5	51.7	60	34	yes
112.2	27.2	0	16	yes
37.1	37	50	49	no
130.2	38.9	48	63	no
39.1	32.5	25	45	yes
81.9	34	12	0	no
24.6	35.8	16	34	no
101.9	32.9	44	42	no
117.6	46.4	62	48	no
148.8	51.9	59	39	yes
60.2	28.9	0	66	no
43.7	35.2	57	77	no
113.1	30.4	70	78	no
38.1	38.3	24	62	no
89.2	49.2	61	0	no
3	21.5	46	83	no
55.8	41.9	10	69	no
89.7	21.8	79	62	no
136.1	66.3	56	34	yes
44.7	28.2	73	77	no
63.2	41.9	64	65	no
163.4	46.7	69	27	yes
64.1	32.1	12	0	no
98.7	38.5	59	77	no
139.9	27.6	0	0	yes
92	47	65	37	no
66.6	20.7	24	51	no
16.4	34	12	75	no
131.9	31.9	76	63	no
11	28	2	42	no
27.9	40	52	84	no
103.5	46.6	26	70	no
107	23.2	11	83	yes
51.6	46.4	53	44	no
133.4	32.1	55	98	yes