linear regression (1 regressor)

what does a regression “trend” represent in a time series model?

the average direction or growth pattern over time—usually how much the outcome increases per period

what does the slope (trend coefficient) tell you in a linear regression?

it shows how much the dependent variable is expected to increase for each time step (ex: per quarter or month)

what does a statistically significant trend mean?

the trend is real and not due to random chance—it likely reflects a genuine pattern in the data

what does a high R-squared value (like 0.91) indicate in regression?

the model explains most of the variation in the data—trend captures a strong part of the overall behavior

what are residuals in a regression model?

the difference between what the model predicts and what actually happened—the leftover error

why do we check residuals after fitting a regression model?

to see if the model is missing patterns—if residuals are correlated, it means the model is not capturing everything

what does a low p-value for the trend coefficient mean?

it means the trend is statistically significant—it likely reflects a real relationship over time

what do AIC and BIC scores tell you about your model?

they measure how well your model fits—lower values are better and can be used to compare models

when would you add a quadratic term to your regression?

when you think the trend may not be straight—if data shows curvature (like speeding up or slowing down)

what does it mean if the quadratic term is not statistically significant?

it means the curve does not add much—a straight line might be enough to explain the data

how can real-world events (like a pandemic) affect trend estimates?

sudden changes can raise or lower the trend, making it seem like the pattern has changed more than it really has

why is forecasting useful in a regression model?

it helps predict future values using past trends—useful in planning, decision-making, or testing scenarios

what does RMSE tell you in model evaluation?

it shows how far off your predictions are from actual values—lower RMSE means better accuracy