Approximation of a func. by the method of least squares

Task # 8 Objective. Approximate the original data given by the table by the method of least squares, using different models of functions and perform a comparison and analysis of the results obtained. To achieve this goal you need to solve the following subtasks. 1) Select the approximating functions, depending on the condition of the problem, justify the choice. 2) Approximate the data with the selected methods, determine the errors of the approximations. 3) Construct a graph of the initial and approximating functions. 4) Analyze the results and select the optimal approximating function. 5) Construct schemes of program algorithms. Option 1.8 The management of some firm that produces electronic devices wants to forecast sales of its products. It is assumed that the explanatory variable may be the costs of research and development (R & D). Data were collected on sales and research costs for 1985-2005: Year of Sale y (thsd.) Research Cost x (Thous. Dollars) 1985 3307 273.4 1986 3556 291.3 1987 3601 306.9 1988 3721 317.1 1989 4036 336.1 1990 4134 349.4 1991 4268 362.9 1992 4578 383.9 1993 5093 402.8 1994 5716 437.0 1995 6357 472.2 1996 6769 510.4 1997 7296 544.5 1998 8178 588.1 1999 8844 630.4 2000 9251 685.9 2001 10006 742.8 2002 11200 801.3 2003 12500 903.1 2004 13101 983.6 2005 13640 1076.7