4. Statistical Techniques Flashcards
Formula for straight line:
y = mx + c
(alternative format) y = a + bx
Always has these components:
- A fixed value - c - This is where the straight line starts.
- A gradient - m - This determines how steep the gradient is and whether it is going up or down (where m is negative)
The formula can be used to predict prices, costs or demand.
The formula for straight line ties in with Hi Lo calcs.
There the fixed value represents the fixed costs, and the gradient value was the variable cost per unit. (Think of the graph representing a semi-variable cost)
Linear regression techniques:
- Average annual change.
- Line of best fit (First and last points do not appear to be representative)
- Least squares method (Not in scope)
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A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).
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(main) factors which can influence data which is generated over a period of time..
- The underlying trend.
This is the way that data is generally moving long term.
Eg. Volume of traffic - Long Term Cycles.
Slow moving variations that may be caused by economic cycles or social trends.
EG. Economic prosperity and Economic depression causing increase/decrease in traffic because of car ownership and trips to work. - Seasonal Variations.
Regular, predictable cycles in the data.
Eg. Not just ‘spring, summer’. Traffic volumes higher in daytime, at weekends etc. - Random variations.
All data will be affected by unpredictable influences.
Eg. Flooding of some roads may reduce traffic in one place but increase on alternative routes. Overall volume may be influenced by heavy snowfall.
NB. For assessment only need underlying trends and seasonal.
To analyse (breakout) data into underlying trends and seasonal variations… stages..
- Deseasonalise the data.
The historical actual data is analysed into the historical trend and the seasonal variations. - Extrapolate the trend.
The historical trend is ued to forecast the future trend, (using techniques..) - Adjust the forecasted trend w/t seasonal variations.
The seasonal variations are incorporated into the forecast future trend to provide forecast of actual data.
Moving averages.
Must include exactly once complete cycle.
The number of ‘points’ is chosen to suit the data.
Eg. Morning, Afternoon, Night-shift.
3-point moving average
Index numbers.
Many government Indices (RPI) and other Indicators are availale
Indicators can be leading or lagging. Eg an index monitoring prices of manufactured goods (‘factory gate’ prices) will react to changes before they have filtered through to retail price indices. The ‘factory gate’ prices can therefore be considered to be a ‘leading’ indicator of retail prices and give early warning of implications to industrial situations.
Make sure index selected is specific enough.
Remember weighting. EG CPI - increase in proportion of household expenditure on holidays
Explain a rime series
Formed by data that occurs over time.
If the data increases or decreases regularly (ie. straigh line) then it can be represented by a formula.
The formula can then be used to predict data at various points
Some data moves in regular cycles over time. Explain the seasonal variations..
.. seasonal variations are the distances that the data is from the underlying trend.
What do you use moving averages for..
.. can be used to split data into the trend and the seasonal variations,
What are index numbers good for?
.. analysing Standard Costing variances to see what part is due to the index change and what is due to another reason (performance)
To create an index when given a series of prices and points and told the base point..
Base point is index 1.
Make sure convert into unit price (probably given a total price and number of kg which will be different each time so need to convert)
Take the new price per unit and divide by the base price per unit and x 100.
