In part (b) the ask us is the model valid? …and why? To answer this, we make use of the ANOVA table that’s provided in output. This is the F-test of validity. I go through all of the steps required for full marks in a hypothesis test including writing the hypotheses, looking up the rejection region on the F-tables, and using the test statistics to decide whether or not to reject the null.
The data in a series of observations taken over time (a time series) can have a lot of variation. Variation leads to unreliable forecasts. To counter this we can use smoothing methods. This question introduces two of them: Exponential Smoothing and the Weighted Moving Average. MAE and MAPE are used to compare their accuracy – plus I’ll show you a third measure of accuracy that sometimes appears on tests: the Mean Squared Error (MSE).
Don't forget to practice minimization questions. This is a question one student asked me regarding how to handle negative coefficients in the constraint of a minimization linear program.
We are investigating whether or not x can help us to predict y. Maybe it does - but does that give us the whole picture? Perhaps OTHER factors also influence the value of y. The coefficient of determination tells us just how much the value of the dependent variable (y) can be determined by the independent variable that we're studying (x).
We can finally solve by comparing the expected value WITH sample information to the cost that the consultants want to charge ($75,000). The final step is then to write out the Optimal Decision Strategy. This is a list of the correct decisions that should be made as we move from the beginning of the decision tree to the end.
In many exam questions, you won’t be asked directly for the coefficient of determination. You’ll need to rely on your understanding of what it measures to know that it’s what you’re being asked to report. I discuss here what the coefficient of determination - and the adjusted coefficient of determination mean in a multiple regression context.
In the previous video we were simply given the value of the Weighted Moving Average as part of the question (Question #2b). Here’s how that value was calculated from the raw data, and how the related MSE was determined from the forecast errors. The Weighted Moving Average appears on a lot of past tests, so it’s important that you can work it out for yourself.