To forecast the result in Year 20 using the regression equation y=6+32xy = 6 + 32xy=6+32x (where xxx is the year):

Substitute x=20x = 20x=20 into the equation: y20=6+3220=646y_{20} = 6 + 32 \times 20 = 646y20=6+3220=646

Interpretation: y20=646y_{20} = 646y20=646 predicts the outcome for Year 20 based on the linear regression model.

Potential Pitfalls:

Forecasting for Year 20 assumes the relationship y=6+32xy = 6 + 32xy=6+32x remains consistent, which may not hold due to:

• Extrapolation Risk: Extending beyond observed data range can lead to inaccurate forecasts.
• Non-linear Trends: If the relationship is not strictly linear, predictions may be biased.
• Data Quality: Fluctuations or outliers not captured in the model can affect accuracy.
• External Factors: Changes outside the model (e.g., economic shifts) could influence results unpredictably.

References:

• Montgomery, D. C., Peck, E. A., & Vining, G. G. (2012). Introduction to Linear Regression Analysis (5th ed.). Wiley.
• Kutner, M. H., Nachtsheim, C. J., Neter, J., & Li, W. (2005). Applied Linear Statistical Models (5th ed.). McGraw-Hill/Irwin.