Quest for linear regression

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Uploaded: 22.05.2013
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1. The dependence of the gross income of commercial enterprises y (mn. Rub. Per year) from the average value of the fixed x (mln. Rub.) And current x (mln. Rub.) Means the number of managerial staff x (pers.) And the size of trading x space (sqm). All OLS assumptions are made. The significance level a = 0.05.
Data
x1 x2 x3 x4 y
34.060 125.172 16.0 388.7 200.18
61.052 140.540 18.0 350.0 247.64
43.279 142.228 11.0 538.8 245.86
72.820 117.490 30.0 326.7 211.91
62.080 98.421 24.0 382.4 165.28
57.034 148.648 13.0 308.8 251.73
50.814 135.584 28.0 593.2 234.83
77.006 155.641 27.0 319.1 268.88
73.496 153.000 22.0 495.7 272.00
69.837 119.193 14.0 426.9 212.01
42.357 84.455 13.0 278.4 139.71
75.229 112.432 27.0 504.5 208.60
68.104 92.591 19.0 535.8 169.64
58.650 147.446 13.0 359.1 251.69
48.592 90.340 20.0 400.4 152.52
34.719 140.220 25.0 556.1 233.76
38.387 145.820 18.0 211.0 242.71
51.494 159.220 15.0 597.9 268.38
41.071 159.473 21.0 429.0 271.39
41.963 125.506 24.0 220.2 199.94
81.449 106.338 25.0 412.5 194.22
55.393 95.294 25.0 277.6 168.07
39.716 98.012 19.0 537.2 169.55
34.224 145.513 12.0 450.7 243.72
34.428 74.078 17.0 463.0 125.47
52.138 104.888 27.0 279.1 176.04
59.520 80.105 10.0 536.9 143.43
61.417 131.256 20.0 249.3 221.51
62.885 76.919 23.0 244.0 138.57
63.144 72.769 18.0 497.3 133.65
41.979 152.394 12.0 325.6 256.31
65.826 96.140 29.0 576.4 169.66
55.638 95.878 29.0 314.4 168.87
50.902 123.442 21.0 334.5 206.21
36.738 132.479 17.0 256.1 224.76
Required
a) To study the correlation between the dependent and explanatory variables. Draw qualitative conclusions about the presence or absence of the pair relationship between y and x, i = 1, ...... 4.
b) Calculate the estimates of the parameters of the linear regression
y = b + bx + bx + bx + bx +
The results are put on a piece of regression. In the output file to copy the values \u200b\u200bof the regression coefficients, the values \u200b\u200band the values \u200b\u200bof Fisher statistics t- statistics.
c) Set the value of the whole depending on the Fisher test, the result is written in the output.
g) Indicate which of the studied variables significantly influence the gross income of enterprises, using Student's t test. Record file "Vyvody.rtf" value statistics for each of the Student regression parameters, and to determine the critical values \u200b\u200bof the Student's statistics, and write it down, pointing df- number of degrees of freedom.
d) Perform point forecast y-values \u200b\u200bfor the company, whose explanatory variables amount to 105% of their value srednevyborochnyh using selective regression equation. The value of Y ^ written conclusions.
e) Add a new variable regression equation x reflecting the work of the working capital and the size of the trading area. Perform processing of items b) - d). Compare the results.

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