Annual high temperatures (Celsius) in a certain location have been tracked for several years on the same date. Let X represent the number of years after 2000 and Y the high temperature. Based on the data shown below, the linear regression equation was calculated using technology.



xy

3

35.47

4

36.66

5

39.35

6

40.34

7

42.33

8

40.12

9

41.51

10

43.6

11

43.99

12

44.88

13

47.77


The equation is y^=33.165+1.036x

Interpret the slope:

For each additional 33.165 years, the annual high temperature will increase by 1 degree on average.

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

For each additional 1.036 years, the annual high temperature will increase by 1 degree on average.

For each additional year, the annual high temperature will increase by 33.165 degrees on average.

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).

Annual high temperatures (Celsius) in a certain location have been tracked for several years on the same date. Let X represent the number of years after 2000 and Y the high temperature. Based on the data shown below, the linear regression equation was calculated using technology. The equation is y^=33.165+1.036x. Interpret the slope: For each additional 33.165 years, the annual high temperature will increase by 1 degree on average. For each additional year, the annual high temperature will increase by 1.036 degrees on average. For each additional 1.036 years, the annual high temperature will increase by 1 degree on average. For each additional year, the annual high temperature will increase by 33.165 degrees on average.

Learn how to interpret the slope of the linear regression equation y^=33.165+1.036x. In this example, the annual high temperatures are tracked over several years, and the slope indicates that for each additional year, the temperature will increase by 1.036 degrees Celsius. Suitable for Grades 10-12.

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