To construct a scatterplot and identify the mathematical model that best fits the given data, you can plot the Dow Jones Industrial Average (y-axis) against the year (x-axis).
Based on the plot, the best fitting model appears to be a quadratic model. A quadratic model is a polynomial equation of the form y = ax^2 + bx + c, where a, b, and c are constants. The curve of a quadratic model is shaped like a parabola.
To find the best predicted value for the year 2006, you can use the quadratic model to predict the Dow Jones Industrial Average for that year. The actual high value for 2006 was 12,464, so you can compare this value to your predicted value to see how good the prediction was.
The pattern in the data suggests that the stock market has been steadily increasing over time. This may be a good indication for investment purposes, as it suggests that the stock market has historically been a profitable place to invest.
However, it is important to note that past performance is not necessarily indicative of future results, and it is always important to do your own research and carefully consider the risks before making any investment decisions.