Using the Data in the Table, First Plot the Data

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The Answer is Data are highly seasonal as the graph and data table indicate. $Data are highly seasonal as the graph and data table indicate. Peaks near 50 occur at points 8, 25 and 42, and this seasonality is reflected in the other significant features of the graph, e.g., lows near -20 at points 10, 27 and 44. The data are rearranged in this table into three 17 observation rows (since 17 is the period of this function)with a seasonal average and seasonal relative appended to the right. The overall average for the data is 13.828; the column labeled Seasonal is each average divided by the 13.828 figure. \begin{array}{|c|c|c|c|c|c|c|c} ext { Time } & ext { Output } & ext { Time } & ext { Output } & ext { Time } & ext { Output } & ext { Average } & ext { Seasonal } \ \hline 1 & 12.5 & 18 & 11.3 & 35 & 11.9 & 11.9 & 0.861 \ \hline 2 & 14.8 & 19 & 13.7 & 36 & 13.5 & 14.0 & 1.012 \ \hline 3 & 15.3 & 20 & 16.3 & 37 & 16.5 & 16.0 & 1.159 \ \hline 4 & 15 & 21 & 13.1 & 38 & 14 & 14.0 & 1.015 \ \hline 5 & 11.5 & 22 & 10.8 & 39 & 11 & 11.1 & 0.803 \ \hline 6 & 11.6 & 23 & 10.3 & 40 & 11.3 & 11.1 & 0.800 \ \hline 7 & 12.8 & 24 & 11 & 41 & 11.1 & 11.6 & 0.841 \ \hline 8 & 51.9 & 25 & 51.4 & 42 & 52.5 & 51.9 & 3.756 \ \hline 9 & 11 & 26 & 11.6 & 43 & 11.3 & 11.3 & 0.817 \ \hline 10 & -19.7 & 27 & -19.2 & 44 & -19.3 & -19.4 & -1.403 \ \hline 11 & 11.9 & 28 & 10.6 & 45 & 12 & 11.5 & 0.832 \ \hline 12 & 17.8 & 29 & 16.8 & 46 & 15.5 & 16.7 & 1.208 \ \hline 13 & 20.3 & 30 & 22.5 & 47 & 20.5 & 21.1 & 1.526 \ \hline 14 & 16.4 & 31 & 15.5 & 48 & 16.5 & 16.1 & 1.167 \ \hline 15 & 11.7 & 32 & 11.7 & 49 & 12.5 & 12.0 & 0.865 \ \hline 16 & 11.1 & 33 & 11.9 & 50 & 10.5 & 11.2 & 0.808 \ \hline 17 & 11.9 & 34 & 13 & & & &\ \hline \end{array} Divide each entry in the table by the seasonal relative. Then use linear regression with independent variables ranging from 1-50 to yield the regression equation Output = 14.05629-0.00895 ∗ Time Reseasoning the forecasted values by the seasonal relatives gives the results in the table and the graph below. \begin{array}{|c|c|c|c} ext { Time } & ext { Regression } & ext { Index } & \begin{array}{c} ext { Seasonally } \ ext { Adjusted } \end{array} \ \hline 51 & 13.600 & 0.861 & 11.704 \ \hline 52 & 13.591 & 1.012 & 13.760 \ \hline 53 & 13.582 & 1.159 & 15.748 \ \hline 54 & 13.573 & 1.015 & 13.774 \ \hline 55 & 13.564 & 0.803 & 10.888 \ \hline 56 & 13.555 & 0.800 & 10.848 \ \hline 57 & 13.546 & 0.841 & 11.396 \ \hline 58 & 13.537 & 3.756 & 50.841 \ \hline 59 & 13.528 & 0.817 & 11.055 \ \hline 60 & 13.519 & -1.403 & -18.967 \ \hline 61 & 13.510 & 0.832 & 11.236 \ \hline 62 & 13.501 & 1.208 & 16.305 \ \hline 63 & 13.492 & 1.526 & 20.588 \ \hline 64 & 13.483 & 1.167 & 15.731 \ \hline 65 & 13.474 & 0.865 & 11.661 \ \hline 66 & 13.465 & 0.808 & 10.874 \ \hline 67 & 13.456 & 0.900 & 12.115 \ \hline 68 & 13.448 & 0.861 & 11.573 \ \hline 69 & 13.439 & 1.012 & 13.606 \ \hline 70 & 13.430 & 1.159 & 15.571\ \hline \end{array} The graph below is a plot of the original data for points 1-50 and the forecast points 51-70.$ Peaks near 50 occur at points 8, 25 and 42, and this seasonality is reflected in the other significant features of the graph, e.g., lows near -20 at points 10, 27 and 44. The data are rearranged in this table into three 17 observation rows (since 17 is the period of this function)with a seasonal average and seasonal relative appended to the right. The overall average for the data is 13.828; the column labeled "Seasonal" is each average divided by the 13.828 figure.

\begin{array}{|c|c|c|c|c|c|c|c} ext { Time } & ext { Output } & ext { Time } & ext { Output } & ext { Time } & ext { Output } & ext { Average } & ext { Seasonal } \\hline 1 & 12.5 & 18 & 11.3 & 35 & 11.9 & 11.9 & 0.861 \\hline 2 & 14.8 & 19 & 13.7 & 36 & 13.5 & 14.0 & 1.012 \\hline 3 & 15.3 & 20 & 16.3 & 37 & 16.5 & 16.0 & 1.159 \\hline 4 & 15 & 21 & 13.1 & 38 & 14 & 14.0 & 1.015 \\hline 5 & 11.5 & 22 & 10.8 & 39 & 11 & 11.1 & 0.803 \\hline 6 & 11.6 & 23 & 10.3 & 40 & 11.3 & 11.1 & 0.800 \\hline 7 & 12.8 & 24 & 11 & 41 & 11.1 & 11.6 & 0.841 \\hline 8 & 51.9 & 25 & 51.4 & 42 & 52.5 & 51.9 & 3.756 \\hline 9 & 11 & 26 & 11.6 & 43 & 11.3 & 11.3 & 0.817 \\hline 10 & -19.7 & 27 & -19.2 & 44 & -19.3 & -19.4 & -1.403 \\hline 11 & 11.9 & 28 & 10.6 & 45 & 12 & 11.5 & 0.832 \\hline 12 & 17.8 & 29 & 16.8 & 46 & 15.5 & 16.7 & 1.208 \\hline 13 & 20.3 & 30 & 22.5 & 47 & 20.5 & 21.1 & 1.526 \\hline 14 & 16.4 & 31 & 15.5 & 48 & 16.5 & 16.1 & 1.167 \\hline 15 & 11.7 & 32 & 11.7 & 49 & 12.5 & 12.0 & 0.865 \\hline 16 & 11.1 & 33 & 11.9 & 50 & 10.5 & 11.2 & 0.808 \\hline 17 & 11.9 & 34 & 13 & & & &\\hline\end{array}

Divide each entry in the table by the seasonal relative. Then use linear regression with independent variables ranging from 1-50 to yield the regression equation
Output = 14.05629-0.00895 ∗ Time
Reseasoning the forecasted values by the seasonal relatives gives the results in the table and the graph below.

\begin{array}{|c|c|c|c} ext { Time } & ext { Regression } & ext { Index } & \begin{array}{c} ext { Seasonally } \ ext { Adjusted }\end{array} \\hline 51 & 13.600 & 0.861 & 11.704 \\hline 52 & 13.591 & 1.012 & 13.760 \\hline 53 & 13.582 & 1.159 & 15.748 \\hline 54 & 13.573 & 1.015 & 13.774 \\hline 55 & 13.564 & 0.803 & 10.888 \\hline 56 & 13.555 & 0.800 & 10.848 \\hline 57 & 13.546 & 0.841 & 11.396 \\hline 58 & 13.537 & 3.756 & 50.841 \\hline 59 & 13.528 & 0.817 & 11.055 \\hline 60 & 13.519 & -1.403 & -18.967 \\hline 61 & 13.510 & 0.832 & 11.236 \\hline 62 & 13.501 & 1.208 & 16.305 \\hline 63 & 13.492 & 1.526 & 20.588 \\hline 64 & 13.483 & 1.167 & 15.731 \\hline 65 & 13.474 & 0.865 & 11.661 \\hline 66 & 13.465 & 0.808 & 10.874 \\hline 67 & 13.456 & 0.900 & 12.115 \\hline 68 & 13.448 & 0.861 & 11.573 \\hline 69 & 13.439 & 1.012 & 13.606 \\hline 70 & 13.430 & 1.159 & 15.571\\hline \end{array}

The graph below is a plot of the original data for points 1-50 and the forecast points 51-70. $Data are highly seasonal as the graph and data table indicate. Peaks near 50 occur at points 8, 25 and 42, and this seasonality is reflected in the other significant features of the graph, e.g., lows near -20 at points 10, 27 and 44. The data are rearranged in this table into three 17 observation rows (since 17 is the period of this function)with a seasonal average and seasonal relative appended to the right. The overall average for the data is 13.828; the column labeled Seasonal is each average divided by the 13.828 figure. \begin{array}{|c|c|c|c|c|c|c|c} ext { Time } & ext { Output } & ext { Time } & ext { Output } & ext { Time } & ext { Output } & ext { Average } & ext { Seasonal } \ \hline 1 & 12.5 & 18 & 11.3 & 35 & 11.9 & 11.9 & 0.861 \ \hline 2 & 14.8 & 19 & 13.7 & 36 & 13.5 & 14.0 & 1.012 \ \hline 3 & 15.3 & 20 & 16.3 & 37 & 16.5 & 16.0 & 1.159 \ \hline 4 & 15 & 21 & 13.1 & 38 & 14 & 14.0 & 1.015 \ \hline 5 & 11.5 & 22 & 10.8 & 39 & 11 & 11.1 & 0.803 \ \hline 6 & 11.6 & 23 & 10.3 & 40 & 11.3 & 11.1 & 0.800 \ \hline 7 & 12.8 & 24 & 11 & 41 & 11.1 & 11.6 & 0.841 \ \hline 8 & 51.9 & 25 & 51.4 & 42 & 52.5 & 51.9 & 3.756 \ \hline 9 & 11 & 26 & 11.6 & 43 & 11.3 & 11.3 & 0.817 \ \hline 10 & -19.7 & 27 & -19.2 & 44 & -19.3 & -19.4 & -1.403 \ \hline 11 & 11.9 & 28 & 10.6 & 45 & 12 & 11.5 & 0.832 \ \hline 12 & 17.8 & 29 & 16.8 & 46 & 15.5 & 16.7 & 1.208 \ \hline 13 & 20.3 & 30 & 22.5 & 47 & 20.5 & 21.1 & 1.526 \ \hline 14 & 16.4 & 31 & 15.5 & 48 & 16.5 & 16.1 & 1.167 \ \hline 15 & 11.7 & 32 & 11.7 & 49 & 12.5 & 12.0 & 0.865 \ \hline 16 & 11.1 & 33 & 11.9 & 50 & 10.5 & 11.2 & 0.808 \ \hline 17 & 11.9 & 34 & 13 & & & &\ \hline \end{array} Divide each entry in the table by the seasonal relative. Then use linear regression with independent variables ranging from 1-50 to yield the regression equation Output = 14.05629-0.00895 ∗ Time Reseasoning the forecasted values by the seasonal relatives gives the results in the table and the graph below. \begin{array}{|c|c|c|c} ext { Time } & ext { Regression } & ext { Index } & \begin{array}{c} ext { Seasonally } \ ext { Adjusted } \end{array} \ \hline 51 & 13.600 & 0.861 & 11.704 \ \hline 52 & 13.591 & 1.012 & 13.760 \ \hline 53 & 13.582 & 1.159 & 15.748 \ \hline 54 & 13.573 & 1.015 & 13.774 \ \hline 55 & 13.564 & 0.803 & 10.888 \ \hline 56 & 13.555 & 0.800 & 10.848 \ \hline 57 & 13.546 & 0.841 & 11.396 \ \hline 58 & 13.537 & 3.756 & 50.841 \ \hline 59 & 13.528 & 0.817 & 11.055 \ \hline 60 & 13.519 & -1.403 & -18.967 \ \hline 61 & 13.510 & 0.832 & 11.236 \ \hline 62 & 13.501 & 1.208 & 16.305 \ \hline 63 & 13.492 & 1.526 & 20.588 \ \hline 64 & 13.483 & 1.167 & 15.731 \ \hline 65 & 13.474 & 0.865 & 11.661 \ \hline 66 & 13.465 & 0.808 & 10.874 \ \hline 67 & 13.456 & 0.900 & 12.115 \ \hline 68 & 13.448 & 0.861 & 11.573 \ \hline 69 & 13.439 & 1.012 & 13.606 \ \hline 70 & 13.430 & 1.159 & 15.571\ \hline \end{array} The graph below is a plot of the original data for points 1-50 and the forecast points 51-70.$

Using the Data in the Table, First Plot the Data

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