22576 Chap.10 Advanced Regression and Model Evaluation
Advanced Regression and Model Evaluation
Week 7 extends regression and asks whether a model can be trusted. This chapter shows how to translate log-log and standardised coefficients into business units, how lagged outcomes handle autocorrelation and month effects handle seasonality, and how an interaction term lets one variable change another's effect.
It then covers training and holdout sets, residuals and mean absolute error, and the five regression assumptions with the plots that diagnose them.
These extensions matter most in the individual predictive report, whose rubric asks for model assumptions to be considered and addressed and for performance to be evaluated with suitable metrics.
The chapter therefore pairs each technique with how it is reported: the converted effect in business units, the diagnostic plot that supports it, and the holdout figure that shows how well the model predicts.
What this chapter covers
- 01
Interpreting log-log coefficients
- 02
Interpreting z-score standardised coefficients
- 03
Autocorrelation and lagged outcome variables
- 04
Seasonality and time-based fixed effects
- 05
Interaction terms and conditional effects
- 06
Holdout testing and the five regression assumptions
Worked example · free
Read an interaction between marketing and competition
- 1Low competition (dummy = 0): each marketing dollar adds b1 = $2.50 of sales.
- 1High competition (dummy = 1): the effect is b1 + b3 = 2.5 + 0.9 = $3.40 per marketing dollar.
- 1The high-competition line starts $400 lower but rises $0.90 faster, so they meet at 400 ÷ 0.9 ≈ $444 of marketing.
Key terms
- Autocorrelation
- Correlation between a time series value and its own earlier values, which biases a basic regression.
- Interaction term
- The product of two explanatory variables, added to test whether one changes the other's effect.
- Homoskedasticity
- The assumption that residuals have equal variance across values of the explanatory variable.
- Multicollinearity
- High correlation between explanatory variables, which inflates their coefficients.
- Lagged variable
- The value of a variable from the previous period, used as an explanatory variable in time series regression.
- Training set
- The share of the sample, typically 70 to 80%, on which a model learns its coefficients.
Advanced Regression and Model Evaluation FAQ
How do I interpret a log-log coefficient?
As an approximate percentage effect: a 1% rise in X goes with about a coefficient-sized percentage change in Y. For larger changes use the conversion S = [(1 + %ΔX)^b1 − 1] × 100, which with b1 = 0.8 and a 10% rise gives 7.92% rather than 8%.
How do I spot autocorrelation in residuals?
Plot residuals in time order. If they rise and fall in long waves instead of scattering randomly around zero, each error is following the previous one. The workshop's remedy is to add the lagged outcome, last period's value of Y, as an explanatory variable and check the plot again.
Why is a model tested on a holdout set?
Accuracy measured on the training rows is flattering, because the model has already learned them. Keeping 20 to 30% of the data aside and predicting it afterwards shows how the model performs on unseen data, which is the performance that matters for a business decision.
What is the difference between autocorrelation and seasonality?
Autocorrelation means the current value depends on recent values, such as today's price on yesterday's, and is handled with a lagged outcome variable. Seasonality means calendar cycles drive part of the outcome, such as higher sales in summer, and is handled with time-based fixed effects such as month.
Which regression assumption affects only the p-values?
Normality of residuals. The workshop notes that when residuals are not normally distributed, the accuracy of p-values and confidence intervals suffers, but the estimated coefficients themselves are not affected. A histogram of residuals is the diagnostic, and the result should be mentioned when significance is reported.
Why convert a standardised coefficient back into dollars?
Because a manager cannot act on standard deviations. Multiplying the coefficient by the standard deviation of the outcome, and naming the standard deviation of the explanatory variable, turns the result into a statement such as a $500 rise in marketing going with about $1,200 more sales.
Assessment move
Practise one conversion of each kind, log-log, standardised and interaction, until you can do them without notes. Then rebuild the Week 8 bike-rental workflow and read every residual plot against the five assumptions, writing one line on each. When writing up, place each diagnostic plot next to the sentence that interprets it, so the marker sees the evidence and the conclusion together.
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