Question

As a real estate analyst, you are requested by the manager to construct a simple linear regression for the relationship between the house value (x) and the upkeep spending (y).

(a) Write the simple linear regression equation below.

(b) What are b0 and b1?

(c) Interpret the meanings of b0 and b1.

(d) If the house value (x) is 150, what will the upkeep spending (y) be, using the simple linear regression model 4a?

(e) Draw the scatterplot showing the relationship between the house value (x) and the upkeep spending (y).

Value X	Upkeep Y
237.00	1412.08
153.08	797.20
184.86	872.48
222.06	1003.42
160.68	852.90
99.68	288.48
229.04	1288.46
101.78	423.08
257.86	1351.74
96.28	378.04
171.00	918.08
231.02	1627.24
228.32	1204.76
205.90	857.04
185.72	775.00
168.78	869.26
247.06	1396.00
155.54	711.50
224.20	1475.18
202.04	1413.32
153.04	849.14
232.18	1313.84
125.44	602.06
169.82	642.14
177.28	1038.80
162.82	697.00
120.44	324.34
191.10	965.10
158.78	920.14
178.50	950.90
272.20	1670.32
48.90	125.40
104.56	479.78
286.18	2010.64
83.72	368.36
86.20	425.60
133.58	626.90
212.86	1316.94
122.02	390.16
198.02	1090.84

Answer 1

a.

X - Mx	Y - My	(X - Mx)2	(X - Mx)(Y - My)
62.5115	493.9885	3907.6876	30879.9621
-21.4085	-120.8915	458.3239	2588.1057
10.3715	-45.6115	107.568	-473.0597
47.5715	85.3285	2263.0476	4059.2047
-13.8085	-65.1915	190.6747	900.1968
-74.8085	-629.6115	5596.3117	47100.2919
54.5515	370.3685	2975.8662	20204.1572
-72.7085	-495.0115	5286.526	35991.5436
83.3715	433.6485	6950.807	36153.9259
-78.2085	-540.0515	6116.5695	42236.6177
-3.4885	-0.0115	12.1696	0.0401
56.5315	709.1485	3195.8105	40089.2284
53.8315	286.6685	2897.8304	15431.7954
31.4115	-61.0515	986.6823	-1917.7192
11.2315	-143.0915	126.1466	-1607.1322
-5.7085	-48.8315	32.587	278.7546
72.5715	477.9085	5266.6226	34682.5367
-18.9485	-206.5915	359.0457	3914.599
49.7115	557.0885	2471.2332	27693.705
27.5515	495.2285	759.0852	13644.288
-21.4485	-68.9515	460.0382	1478.9062
57.6915	395.7485	3328.3092	22831.3246
-49.0485	-316.0315	2405.7554	15500.871
-4.6685	-275.9515	21.7949	1288.2796
2.7915	120.7085	7.7925	336.9578
-11.6685	-221.0915	136.1539	2579.8062
-54.0485	-593.7515	2921.2404	32091.3779
16.6115	47.0085	275.9419	780.8817
-15.7085	2.0485	246.757	-32.1789
4.0115	32.8085	16.0921	131.6113
97.7115	752.2285	9547.5372	73501.3751
-125.5885	-792.6915	15772.4713	99552.9364
-69.9285	-438.3115	4889.9951	30650.4657
111.6915	1092.5485	12474.9912	122028.3808
-90.7685	-549.7315	8238.9206	49898.3037
-88.2885	-492.4915	7794.8592	43481.3358
-40.9085	-291.1915	1673.5054	11912.2075
38.3715	398.8485	1472.372	15304.4152
-52.4685	-527.9315	2752.9435	27699.7739
23.5315	172.7485	553.7315	4065.0313
		SS: 124951.7975	SP: 906933.1049

Sum of X = 6979.54
Sum of Y = 36723.66
Mean X = 174.4885
Mean Y = 918.0915
Sum of squares (SS_X) = 124951.7975
Sum of products (SP) = 906933.1049

Regression Equation = ŷ = bX + a

b1 = SP/SS_X = 906933.1/124951.8 = 7.2583

b0 = M_Y - bM_X = 918.09 - (7.26*174.49) = -348.3921

ŷ = 7.2583X - 348.3921

b. b0= -348.3921, b1=7.2583

c. For every increase in x, there is corresponding 7.2583 increase in y

For x=0, y=-348.3921

d. For x=150,

ŷ = (7.2583*150) - 348.3921=740.3529

e.