Until 1985, the number of marriages registered was collected quarterly, at the end of the quarter, by Statistics New Zealand from the Registrar of Births, Deaths and Marriages.
Part A: Trends and forecasting
1. Open the Excel file (dataset above) called Marriage data and use the Marriages A worksheet.
1.1 Smooth the data to find a single trend, using a linear model. Describe the trend in context.
1.2 Discuss how well the trend reflects the data. Explain with reference to the graph.
1.3 Forecast the results for each quarter in 1972, using the linear model. Explain how you arrived at your forecast values and comment on how accurate you think your forecasts are.
2. By looking closely at your graph and data from question 1, find the best model for this trend line.
2.1 Use this model to forecast the number of marriages in each quarter of 1972.
2.2 Evaluate your forecast calculations by looking at the patterns in the data.
3. Now look at the Marriages B worksheet and graph the actual data and moving average.
Evaluate both sets of forecasts from questions 1 and 2 against your results. Explain any discrepancies in terms of the trend and the seasonal component for the new data.
Part B: Using other models for the trend
1. Open the Excel file Marriage data (below) and use the Marriages B worksheet.
1.1 Analyse the data to find a linear model for the trend and draw the graph. Describe the trend in context and discuss how well this reflects the patterns in the data.
1.2 Try some other models and comment on the results.
2 Split the data into two sets.
2.1 Analyse each set separately, using linear models. Try and get the best possible result from the split.
2.2 Describe the trends that you have found in context. How well do the trends reflect the data? Explain with reference to the data and the graph.
2.3 Experiment with other splits, assuming you want to forecast for 1985. Find the best linear model to do this forecast.
2.4 The actual values for 1985 are below. Evaluate your results against these.
Actual values 1985
Mar
7,422
Jun
5,833
Sept
4,405
Dec
6,997
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