The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of

electricity used (in kilowatts).

Temperature (x)	Kilowatts (y)
73	680
78	760
85	910
98	1510
93	1170
83	888
92	923
81	837
76	600
105	1800
Based on your results, If the temperature increases by 1 degree, Kilowatts, on average, increases by approximately how much? Round to 3 decimal places.


To determine the average increase in electricity usage (in kilowatts) per degree increase in temperature, we can use **linear regression**. The slope of the best-fit line will tell us how much the kilowatt usage increases for each degree increase in temperature.

We can calculate the slope (denoted as \(m\)) using the formula for linear regression:

\[
m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}
\]

Where:
- \(n\) is the number of data points.
- \(x\) is the temperature.
- \(y\) is the kilowatt usage.

Let me calculate that for you.The slope of the best-fit line is approximately \( 34.858 \). This means that for every 1-degree increase in temperature, the kilowatt usage increases by approximately **34.858 kilowatts**, on average.

Would you like to see further details or have any questions?

Here are 5 related questions to expand on this information:
1. What would the electricity usage be at 100 degrees Fahrenheit based on this model?
2. How do we interpret the y-intercept of the regression line in this context?
3. How can we check the strength of the linear relationship using correlation?
4. What would happen if we included more data points with extreme temperatures?
5. How does linear regression help in making predictions in other fields?

**Tip:** When interpreting regression results, always check the fit of the model (e.g., R-squared) to ensure the relationship is strong enough for predictions.

The city of Oakdale wishes to see if there is a linear relationship between the temperature and the amount of electricity used (in kilowatts). Temperature (x) Kilowatts (y) 73 680, 78 760, 85 910, 98 1510, 93 1170, 83 888, 92 923, 81 837, 76 600, 105 1800. Based on your results, If the temperature increases by 1 degree, Kilowatts, on average, increases by approximately how much? Round to 3 decimal places.

Discover how to calculate the linear relationship between temperature and electricity usage in Oakdale using linear regression. This solution demonstrates how each degree increase in temperature leads to an average increase of 34.858 kilowatts. Learn the key concepts of linear regression and slope calculation, suitable for students in Grades 10-12.

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