Question

IBM AAPL MSFT
106.12 40.25 110.75
109.00 39.38 58.00
120.00 41.25 73.00
117.50 44.75 76.00
111.50 42.00 66.50
101.87 37.00 61.50
106.37 29.00 63.00
105.50 30.75 63.75
113.62 36.75 72.25
113.00 43.00 75.25
126.75 55.50 98.12
128.75 57.25 103.75
113.87 68.00 106.12
103.00 55.00 99.00
106.12 47.00 109.75
97.12 41.50 68.12
101.25 46.25 73.50
96.87 53.00 85.25
103.62 49.50 89.00
98.25 51.50 93.87
92.50 50.75 97.25
89.00 56.38 111.25
90.00 64.75 120.25
86.87 67.50 123.50
83.50 58.25 118.50
90.75 60.13 110.25
90.75 59.75 121.00
97.87 48.00 70.00
94.75 46.75 72.75
86.62 46.00 74.50
80.75 45.13 80.50
66.87 52.50 88.75
68.25 57.50 93.12
50.38 59.75 85.37
51.50 59.50 86.50
54.38 53.00 83.37
50.88 51.50 92.50
48.63 51.25 85.50
52.75 56.63 92.62
49.38 39.50 88.00
44.50 27.75 74.00
45.75 26.50 75.12
42.00 23.37 82.50
46.00 30.75 80.12
53.88 31.50 80.00
56.50 29.25 80.62
56.50 32.75 85.12
52.88 36.50 82.50
54.63 33.25 84.75
57.50 30.00 92.50
63.00 29.25 53.75
58.75 26.50 51.63
61.88 33.69 51.50
68.50 36.19 58.13
69.62 33.69 56.13
74.50 43.19 63.00
70.75 37.25 62.88
73.50 39.00 61.13
72.12 40.38 59.38
75.25 39.50 63.00
82.12 35.25 71.12
94.62 38.25 81.75
93.00 41.56 84.69
96.00 46.44 90.37
108.87 45.00 90.50
103.37 43.00 92.50
94.50 37.25 90.50
97.25 36.31 100.00
96.62 38.13 87.12
91.37 31.87 87.75
108.50 27.62 92.50
122.62 27.50 98.69
111.25 24.56 103.12
107.75 24.37 113.25
106.75 26.12 118.75
99.00 21.00 120.12
107.50 22.00 117.87
114.37 24.25 122.50
124.50 22.19 131.88
129.00 23.00 137.25
159.38 24.12 156.88
151.50 20.87 82.62
156.88 16.62 102.00
143.75 16.25 97.50
137.25 18.25 91.69
160.50 17.00 121.50
86.50 16.62 124.00
90.25 14.25 126.37
105.75 17.50 141.38
101.37 21.75 132.19
106.00 21.69 132.31
98.50 17.03 130.00
109.50 17.75 141.50
104.62 13.13 129.25
98.75 18.31 149.19
104.44 23.62 84.75
103.87 27.50 89.50
115.87 27.37 90.12
117.50 26.62 84.81
114.81 28.69 108.37
132.50 34.63 109.94
112.62 31.19 95.94
128.50 38.13 110.06
148.50 37.13 105.87
165.13 31.94 122.00
184.38 40.94 138.69
183.25 41.19 175.00
169.75 34.81 150.13
177.25 35.94 89.62
209.19 46.00 81.31
116.00 44.06 80.69
129.25 46.31 90.19
125.69 55.69 85.81
124.56 65.25 92.56
121.00 63.31 90.56
98.25 80.12 92.56
103.06 97.87 91.05
107.87 102.81 116.75
112.25 103.75 97.87
102.75 114.62 89.37
118.37 135.81 106.25
111.50 124.06 69.75
107.31 84.00 62.56
109.56 52.38 80.00
112.25 50.81 69.81
132.02 60.94 69.81
112.62 25.75 60.31
98.50 19.56 68.87
93.50 16.50 57.38
85.00 14.88 43.38
112.00 21.62 61.06
99.90 18.25 59.00
96.18 22.07 54.69
115.14 25.49 67.75
111.80 19.95 69.18
113.50 23.25 73.00
105.21 18.79 66.19
99.95 18.55 57.05
91.72 15.51 51.17
108.07 17.56 58.15
115.59 21.30 64.21
120.96 21.90 66.25
107.89 24.72 63.71
98.12 21.70 58.34
104.00 23.67 60.31
83.76 24.27 52.26
80.45 23.30 50.91
72.00 17.72 54.70
70.40 15.26 47.98
75.38 14.75 49.08
58.31 14.50 43.74
78.94 16.07 53.47
86.92 15.50 57.68
77.50 14.33 51.70
78.20 14.36 47.46
77.95 15.01 23.70
78.43 14.14 24.21
84.90 14.22 25.57
88.04 17.95 24.61
82.50 19.06 25.64
81.25 21.08 26.41
82.01 22.61 26.52
88.33 20.72 27.80
89.48 22.89 26.14
90.54 20.91 25.71
92.68 21.37 27.37
99.23 22.56 27.65
96.50 23.92 26.53
91.84 27.04 24.93
88.17 25.78 26.13
88.59 28.06 26.23
88.15 32.54 28.56
87.07 32.34 28.49
84.69 34.49 27.30
85.74 38.75 27.65
89.75 52.40 27.97
94.24 67.05 26.81
98.58 64.40 26.72
93.42 76.90 26.28
92.58 44.86 25.16
91.38 41.67 24.17
76.38 36.06 25.30
75.55 39.76 25.80
74.20 36.81 24.84
83.46 42.65 25.61
80.62 46.89 27.38
80.22 53.61 25.73
81.88 57.59 25.70
88.90 67.82 27.68
82.20 71.89 26.15
81.30 75.51 28.15
80.24 68.49 26.87
82.47 62.72 27.21
82.34 70.39 24.15
79.90 59.77 22.65
76.82 57.27 23.30
77.41 67.96 24.06
80.97 67.85 25.70
81.94 76.98 27.35
92.33 81.08 28.71
91.92 91.66 29.36
97.15 84.84 29.86
99.15 85.73 30.86
92.94 84.61 28.17
94.26 92.91 27.87
102.21 99.80 29.94
106.60 121.19 30.69
105.25 122.04 29.47
110.65 131.76 28.99
116.69 138.48 28.73
117.80 153.47 29.46
116.12 189.95 36.81
105.18 182.22 33.60
108.10 198.08 35.60
107.11 135.36 32.60
113.86 125.02 27.20
115.14 143.50 28.38
120.70 173.95 28.52
129.43 188.75 28.32
118.53 167.44 27.51
127.98 158.95 25.72
121.73 169.53 27.29
116.96 113.66 26.69
92.97 107.59 22.33
81.60 92.67 20.22
84.16 85.35 19.44
91.65 90.13 17.10
92.03 89.31 16.15
96.89 105.12 18.37
103.21 125.83 20.26
106.28 135.81 20.89
104.42 142.43 23.77
117.93 163.39 23.52
118.05 168.21 24.65
119.61 185.35 25.72
120.61 188.50 27.73
126.35 199.91 29.41
130.90 210.73 30.48
122.39 192.06 28.18
127.16 204.62 28.67
128.25 235.00 29.29
129.00 261.09 30.54
125.26 256.88 25.80
123.48 251.53 23.01
128.40 257.25 25.81
123.13 243.10 23.47
134.14 283.75 24.49
143.60 300.98 26.67
141.46 311.15 25.26
146.76 322.56 27.91
162.00 339.32 27.73
161.88 353.21 26.58
163.07 348.51 25.39
170.58 350.13 25.92
168.93 347.83 25.01
171.55 335.67 26.00
181.85 390.48 27.40
171.91 384.83 26.60
174.87 381.32 24.89
184.63 404.78 26.63
188.00 382.20 25.58
183.88 405.00 25.96
192.60 456.48 29.53
196.73 542.44 31.74
208.65 599.55 32.26
207.08 583.98 32.02
192.90 577.73 29.19
195.58 584.00 30.59
195.98 610.76 29.47
194.85 665.24 30.82
207.45 667.10 29.76
194.53 595.32 28.54
190.07 585.28 26.62
191.55 532.17 26.71
203.07 455.49 27.45
200.83 441.40 27.80
213.30 442.66 28.61
202.54 442.78 33.10
208.02 449.73 34.90
191.11 396.53 34.54
195.04 452.53 31.84
182.27 487.22 33.40
185.18 476.75 33.28
179.21 522.70 35.41

IBM Case: Regression Analysis & Model Building To manage an investment portfolio, you are required to analyze and predict prices of intrading stocks of IBM (International Business Machines Corp., which is the dependent variable for regression analysis). A sample of historical records of 284 periods’ monthly stock closing prices of the company is given for analysis, which is listed in the attached Excel dataset “IBM.xls”, with variable name of IBM.

Also based on experts’ opinions, the following two potential independent variables may have influences on IBM stock prices:

AAPL: monthly stock closing price of Apple Inc.

MSFT: monthly closing price of stock of Microsoft Corp.

Monthly closing prices of all independent variables are listed in the same Excel dataset, in columns after that of the IBM. Now use the data given, and with significance levels of  = 0.05, applying the following analysis procedures:

(a). Construct a multiple linear regression with the data given, write down (type) this linear regression model estimate using correct format.

(b). Interpret the meaning of any partial regression coefficient estimate in the previous model you identified.  

(c). Using Global-F test, testing the overall significance of the regression model you identified in (a).  

(d). What is the R2 of the regression model in (a)? Interpret its meaning.  

(e). Obtain the predicted IBM stock closing price values using the regression model you built in (a), based on historical data given, provide an overlay plot of both observed and predicted IBM values.

Answer 1

Let Y denote the IBM stock price.
Let X1 denote the Apple stock price
Let X2 denote the Microsoft stock price

PART (a)

The multiple linear regression model is given as,

for i =1,2,.. 248

where,

the estimated regression model is obtained as,

Part (b)

denotes the change in per unit change in when the effect of the oother variables are kept constant.

is the intercept or the value of yi when the effect of the variables x1i and x2i are not present

Part(c)

The value of the F statistic to check for the significance of the regression equation is obtained as 277.3 with 2 and 281 degrees of freedom. With p-value<2.2x10^-16 <0.05
thus in light of the given data, the model c is said to be significant.

Part (d)

the value of is obtained as 0.6673 .i.e. 66.73% of variability in Y can be explained the above regression model.