Annual high temperatures in a certain location have been tracked for several years. Let 
 represent the year and 
 the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).

y = 
 x + 


x	y
4	28.78
5	24.2
6	22.92
7	22.44
8	19.66
9	16.68
10	15.9
11	10.82
12	8.94
13	8.16
14	7.98
15	2.7


 numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression

# Data
x = np.array([4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]).reshape(-1, 1)
y = np.array([28.78, 24.2, 22.92, 22.44, 19.66, 16.68, 15.9, 10.82, 8.94, 8.16, 7.98, 2.7])

# Linear regression model
model = LinearRegression()
model.fit(x, y)

# Coefficients
slope = model.coef_[0]
intercept = model.intercept_

slope, interceptThe regression line for the given data is:

\[
y = -2.21x + 36.72
\]

Would you like details on how this regression line was calculated or any further analysis?

### Relative Questions:
1. What does the slope of the regression line indicate in this context?
2. How can we interpret the y-intercept in this regression equation?
3. Could this regression line be used to predict future temperatures, and what are the limitations?
4. How well does the regression line fit the data? Would you like me to calculate \( R^2 \)?
5. What happens to the temperature as the years progress based on this model?

### Tip:
Always check the goodness-of-fit of a regression line to understand how well it represents the data.

Annual high temperatures in a certain location have been tracked for several years. Let x represent the year and y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places).

Learn how to calculate the regression line for annual high temperatures with data points for years and temperatures. The solution uses linear regression, providing detailed steps with a focus on statistical concepts. Suitable for Grades 10-12.

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