In what follows we assume that an intercept is always included in the model. The intercept should always be included unless the requirement is to force the regression line “through the origin”. Without it, the slope coefficient can be distorted unnecessarily. Even when \(x=0\) does not make sense, the intercept is an important part of the model. In this case when \(x=0\) (i.e., when there is no change in personal disposable income since the last quarter) the predicted value of \(y\) is 0.55 (i.e., an average increase in personal consumption expenditure of 0.55%). The interpretation of the intercept requires that a value of \(x=0\) makes sense. Alternatively the estimated equation shows that a value of 1 for \(x\) (the percentage increase in personal disposable income) will result in a forecast value of \(0.55 0.28 \times 1 = 0.83\) for \(y\) (the percentage increase in personal consumption expenditure). The slope coefficient shows that a one unit increase in \(x\) (a 1 percentage point increase in personal disposable income) results on average in 0.28 units increase in \(y\) (an average increase of 0.28 percentage points in personal consumption expenditure). The fitted line has a positive slope, reflecting the positive relationship between income and consumption. We will discuss how tslm() computes the coefficients in Section 5.2. Tslm(Consumption ~ Income, data=uschange) #> #> Call: #> tslm(formula = Consumption ~ Income, data = uschange) #> #> Coefficients: #> (Intercept) Income #> 0.545 0.281 12.9 Dealing with missing values and outliers.12.8 Forecasting on training and test sets.12.7 Very long and very short time series.12.5 Prediction intervals for aggregates.12.3 Ensuring forecasts stay within limits.10.7 The optimal reconciliation approach.10 Forecasting hierarchical or grouped time series.9.4 Stochastic and deterministic trends.7.5 Innovations state space models for exponential smoothing.7.4 A taxonomy of exponential smoothing methods.6.7 Measuring strength of trend and seasonality.5.9 Correlation, causation and forecasting.1.7 The statistical forecasting perspective.1.6 The basic steps in a forecasting task.
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