Reduce to the simplest form
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The analysis of time series is a process by which a set of observations in a time series is analyzed.
Part a: The time series plot is constructed both in de$mo$ and excel sheet.
b. The data appear to follow a horizontal pattern.
Part b: The trial and error is used to find the value of exponential smoothing coefficient that results in MSE= 0.009 which is less than 0.01.
The MSE in the first table is calculated using the average of the two previous years.
The MSE in the second table is calculated using the moving average
The MSE in the third table is calculated by using ∝= 0.4 and the value of alpha changes to different values as shown in the cell U20, V20 and W20.
The MSE is the mean squared error.
We find the error by subtracting <u><em>forecast</em></u> data from the <em><u>actual</u></em> data.
The forecasted data may be average of 2 years , moving average of 3 years or adding the multiplied chosen value of alpha with the actual data and the multiplied value of 1- ∝ with the forecasted value of data.
The error is then squared.
The squared error is then averaged which gives the MSE.
The values of ∝= 0.400641005, 0.40319659, 0.400641001 may give the best MSE values.
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So essentially, this is a cubic function where T(x) = y, and:
In order to find the vertices, aka "turning points", we need to see around what area the graph will curve quickly from bottom-left to top-right. If the value being cubed (in the parentheses) is around -8, y will be close to 0, since -8+7=-1. (-2)^3 = -8. So x+5=-2, x=-7.
At x=-6, y = (-6+5)^3+7 = (-1)^3+7
y = -1+7 = 6
At x=-5, y = 0+7 = 7
Above x=-4, the y jumps rapidly above 10, and below x=-9, the y jumps rapidly below -50
What does all that mean???
That between x = -9 and x = -4 (x = -4,-5,-6,-7,-8,-9), the temperature (T(x) or y) does not change very much. Therefore, around those temperatures is a turning point, where the phase shift occurs from solid/liquid.
In order to find the vertices, aka "turning points", we need to see around what area the graph will curve quickly from bottom-left to top-right. If the value being cubed (in the parentheses) is around -8, y will be close to 0, since -8+7=-1. (-2)^3 = -8. So x+5=-2, x=-7.
At x=-6, y = (-6+5)^3+7 = (-1)^3+7
y = -1+7 = 6
At x=-5, y = 0+7 = 7
Above x=-4, the y jumps rapidly above 10, and below x=-9, the y jumps rapidly below -50
What does all that mean???
That between x = -9 and x = -4 (x = -4,-5,-6,-7,-8,-9), the temperature (T(x) or y) does not change very much. Therefore, around those temperatures is a turning point, where the phase shift occurs from solid/liquid.