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Week 7 Regression Models for Prediction - Coggle Diagram
Week 7 Regression Models for Prediction
Regression when data is recorded over time
Mostly we've been using regression to see how a variable effects another
Eg. How education affects income
Another use for regression is for prediction and forecasting
Forecasting is important for a data series that has been indexed over time
Eg. production, unemployment, inflation, sales
Componenets of a time series
Trend
A persistent, long term, upward or downward pattern of movement
Duration is usually several years
Cycle
A pattern of up and down swings that tend to repeat every 2-10 years
Seasonal
A seasonal pattern is a regular pattern of fluctuations that happen within a year
Irregular
This component represents whatever is left over after identifying the other 3 systematic components
Analyzing the components of a time series
In order to analyze the components of a time series a regression model needs to be plotted
We need to create a time variable the ascends by 1 on each entry, and estimate a regression model with this as the x variable
The coefficient of this time will tell us how much the y variable changes with a change in time
The intercept represents the estimated value of y on a when time = 0 or a time period before the first one. (h
owever this prediction will be quite wrong because the slope is not considering seasonal patterns)
in order to get a more accurate prediction that accounts for seasonality dummy variables need to be created for the quarters q1, q2, q3 while q4 is omitted
We plot a regression model with time as well as the dummy variables as the x variable
The values in the regression statistics from the individual quarters will be in relation to the omitted statistic
Forecasting
We can use our model to predict the value of y in future time periods
We can simply do this by adding the known values to the equation of the regression model, including the dummy variables