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In: Statistics and Probability

The quarterly sales data (number of book sold) for Christian book over the past three years...

The quarterly sales data (number of book sold) for Christian book over the past three years in California follow:

    Year 1               Year 2               Year 3

  1.   1690              1800                  1850
  2.   940                 900                   1100
  3.   2625              2900                  2930
  4.   2500             2360                   2615

1. Construct a time series plot. What type of pattern exists in the data? This was not shown in the WebEx example I provided. But you can simply create this graph in Excel (Go to INSERT and look for charts under INSERT Tab). Basically you need to provide a 2-dimensional graph showing the trend of book sales over the given time period. The vertical line represents sale for Christian book, while the horizontal line represents quarter.

2. Use the following dummy variables to develop an estimated regression equation to account for any seasonal effects in the data: Quarter1=1 if the sales data point is in Quarter 1, otherwise Quarter 1=0; Quarter 2=1 if the sales data point is in Quarter 2, otherwise, Quarter 2=0; Quarter 3=1 if the sales data point is in Quarter 3, otherwise Quarter 3=0.

3. Compute the quarterly forecasts for next year.

4. Let t=1 to refer to the observation in quarter 1 of year 1; t=2 to refer to the observation in quarter 2 of year 1;,,,, and t=12 to refer to the observation in quarter 4 of year 3. Using the dummy variables defined in part (2) and t, develop an estimated regression equation to account for seasonable effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute the quarterly forecasts for next year.

Solutions

Expert Solution

Ans-  

Year 1 Year 2 Year 3
1690 1800 1850
940 900 1100
2625 2900 2930
2500 2360 2615

(1)- Here the line graph make by excel where the vertical line represents sale for Christian book, while the horizontal line represents quarter for the given data.

(2)-

sales Period Quarter 1 Quarter 2 Quarter 3 Quarter 4
1690 1 1 0 0 0
940 2 0 1 0 0
2625 3 0 0 1 0
2500 4 0 0 0 1
1800 5 1 0 0 0
900 6 0 1 0 0
2900 7 0 0 1 0
2360 8 0 0 0 1
1850 9 1 0 0 0
1100 10 0 1 0 0
2930 11 0 0 1 0
2615 12 0 0 0 1

here for this data below are given the regression output

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.989744
R Square 0.979592
Adjusted R Square 0.846939
Standard Error 124.9667
Observations 12

and

Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 2491.667 72.14954 34.53476 5.4E-10 2325.29 2658.044 2325.29 2658.044
Quarter 1 -711.667 102.0349 -6.97474 0.000116 -946.959 -476.374 -946.959 -476.374
Quarter 2 -1511.67 102.0349 -14.8152 4.24E-07 -1746.96 -1276.37 -1746.96 -1276.37
Quarter 3 326.6667 102.0349 3.20152 0.012584 91.37388 561.9595 91.37388 561.9595

hence the estimated regression line is Y= sales , and X = quarter

(3) quarterly forecast for next year

Quarter 1 1780
Quarter 2 980
Quarter 3 2818.333
Quarter 4 2491.667

orchestra answered 1 year ago
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