# Penguin Parade. Quantitative description [A] – The linear equation is y = -43.244x + 2154.3 – On average, the number of penguins marching is decreasing.

## Presentation on theme: "Penguin Parade. Quantitative description [A] – The linear equation is y = -43.244x + 2154.3 – On average, the number of penguins marching is decreasing."— Presentation transcript:

Quantitative description [A] – The linear equation is y = -43.244x + 2154.3 – On average, the number of penguins marching is decreasing by 43 penguins per quarter. (YOU MUST ROUND THIS ANSWER!!! 44 Penguins would be acceptable also.)

Penguin Parade Forecasts – Needed 2 correct out of the 3 [M] Forecast = Trend + ASE 1.Forecast for March 2009 = -43.244 x 33 + 2154.3 +-299 = 428.248 I forecast that in March 2009 there will be 428 penguins marching per quarter. 2.Forecast for June 2009 = -43.244 x 34 + 2154.3 +-290 = 394.004 I forecast that in June 2009 there will be 394 penguins marching per quarter. 3.Forecast for September 2009 = -43.244 x 35 + 2154.3 +-380 = 260.76 I forecast that in September 2009 there will be 261 penguins marching per quarter. 4.Forecast for December 2009 = -43.244 x 36 + 2154.3 +970 = 1567.516 I forecast that in December 2009 there will be 1568 penguins marching per quarter.

Penguin Parade Describe at least one further feature [E] – Seasonal variation: Penguin numbers peak every December then sharply decrease with the lowest numbers in the September quarter. – Reasons could be: Dec increase – Go back home for nesting, mating, and hatching, more that were out gathering food return to the area, favourable (warmer ) weather conditions, possibly lower predator numbers. Drop after Dec as penguins leave to go back into the sea or die, low in Sept as they stay in the sea to feed.

Penguin Parade Describe at least one further feature [E] – Ramp around December 2003 to March 2004 where there is a significant drop in the number of penguins marching – Possible reasons: change in conditions due to disease, human development in the area, chemical dumping, introduction of predators, sudden depletion of food supply – No obvious outliers

Penguin Parade Relevance and usefulness of the forecasts [E] – Forecast useful to conservationists to study if penguin numbers are decreasing or increasing and how other natural or manmade factors may be influencing the numbers. – Information may be useful for tourist operators as a possible attraction. – Info could be useful for Government departments indicating a possible need for funding. – However, the information is only for a short period and needs to go further back to see overall trends. – Relevant only for that area as conditions may be different in other places.

Penguin Parade Appropriateness of the model [E] – The linear trendline has an R 2 value of 0.82 indicating that it is a reasonable fit for the data. However, the CMM values show a pattern of fluctuating from being below the trendline to being above the trendline which indicates that the trendline is not appropriate for making forecasts. – Also, if the decreasing trend continues, eventually the model will predict a negative value for the number of penguins that are marching. – It would not be appropriate to use this model to predict far into the future. – Need more data to see what patterns emerge in the increase/decrease.

Penguin Parade Possible Improvements [E] – Due to the large ramp and the fact that more recent data is more relevant, it makes sense to try to fit a piecewise model and use the trendline based on the recent values to make predictions. – When I did this, the trendline based on the most recent data fit the points extremely well and the R 2 value was high at 0.982 indicating that it is a good fit for the data. However, since we have very limited data we still cannot be certain of the long term trend, and should not use this model to make predictions far in the future. It would be more suitable than the simple linear trend however for making predictions in the short term.

Penguin Parade Limitations of the Analysis [E] – As this data was collected around Phillip Island, it would not be appropriate for forecasting penguin numbers marching in other areas. – We only have 6 years of data. If we had more data we would be able to get a better idea of the long term trend as it seems like there has been a shift. We don’t know if this shift is due to a permanent change (possibly in the climate or local environment) or perhaps it is cyclical in nature. Having data over a longer period of time may enable us to identify what the long term trend actually is and therefore have a better model for forecasting.

Penguin Parade Interpretation of the seasonally adjusted data [E] – Seasonally adjusted data shows higher than expected numbers in June 2002 and Dec 2003 Dec 2003 and June 2002 - could be due to favourable (warm) weather effect – Lower than expected values in Dec 2001 and Mar 2004 Dec 2001 - could be due to disease or a food shortage Mar 2004 shows a BIG drop so a serious event occurred such as a cyclone, development in the area, disease, or an oil spill

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