The correct interpretation of the slope in the equation $\hat{y} = 33.165 + 1.036x$ is:

For each additional year, the annual high temperature will increase by 1.036 degrees on average.

The slope (1.036) represents the rate of change of the temperature per year. This means that for every 1-year increase in $x$ (the number of years after 2000), the temperature $y$ is predicted to increase by approximately 1.036 degrees Celsius.

Would you like further clarification or have any additional questions?

Here are 5 related questions to deepen understanding:

1. How would you interpret the intercept (33.165) in this context?
2. If the slope were negative, what would that indicate about temperature trends over time?
3. How could you use this equation to predict the temperature in 2025?
4. What are the potential limitations of using linear regression for long-term temperature predictions?
5. What role do outliers play in affecting the accuracy of a linear regression model?

Tip: In a regression equation, the slope tells you how much the dependent variable (e.g., temperature) changes for each unit increase in the independent variable (e.g., years).