Task №1. For the data presented in the table is required:
1. Construct a scatterplot from, depending on x1 and x2.
2. Calculate the matrix of pairwise correlation coefficients, to evaluate the statistical significance of the correlation coefficients.
3. calculation, using the method of least squares, the parameters of the linear multiple regression equation with the complete list of factors.
4. Select the factors in the model (specified in paragraph 4: as the threshold value of the correlation coefficient of the pair, the resulting index and each of the factors to take 0.6, and the threshold of the pair correlation coefficient factor of 0.9).
5. Evaluate by the method of least squares linear regression parameters of the equation.
6. Calculate the value of the result predicted by both models, if the predicted value factors of 80% of their maximum values.
Month Volume of sales (thousand. Rub.) TV advertising Newspaper advertising
1 15304 133 38
2 17554 152 32
3 16876 130 35
4 16435 165 44
5 15229 125 48
6 16986 158 37
7 17914 165 43
8 16817 149 38
9 16579 169 28
10 15330 137 39
11 16781 178 42
12 17008 147 37

Problem №2. For the time series yt is required:
1. Check for anomalous observations.
2. Construct a linear model whose parameters are estimated using the least squares method.
3. Assess the adequacy of the model constructed using the residual components of the independence property, accident and matching normal distribution using the R / S to take the criterion tabulated border 2.7 and 3.7.
4. Assess the accuracy of the model through the use of an average relative error of approximation e-relative.
5. To carry out the forecast for 2 steps forward.
6. The actual value of the indicator, the results of modeling and forecasting represented graphically.
21.2
21.2
28.2
34.1
39.1
43.1
47
54
54