numpy as np from sklearn.linear_model import LinearRegression

Data

years = np.array([1950, 1960, 1970, 1980, 1990, 2000, 2005]).reshape(-1, 1) life_expectancy = np.array([71.6, 72.4, 75.8, 76.6, 78.4, 81.6, 82.4])

Fit linear regression model

model = LinearRegression() model.fit(years, life_expectancy)

Regression line equation: y = mx + b

m = model.coef_[0] # slope b = model.intercept_ # y-intercept

Predict life expectancy for 2007

prediction_2007 = model.predict([[2007]])[0]

m, b, prediction_2007### Part 1: Regression Line The regression line equation is:

$y = 0.20102x - 320.90425$

(Simplified to five decimal places).

Part 2: Prediction for 2007

Using the regression line, the predicted life expectancy of women in 2007 is approximately:

$82.5 \, \text{years}$

(Simplified to one decimal place).

Would you like further details or have any questions? Here are 5 related questions:

1. How is the regression line derived from the data?
2. Why is linear regression appropriate for this dataset?
3. What other methods could we use to predict life expectancy trends?
4. How accurate is this prediction likely to be, given the data?
5. Could we use this model to predict life expectancy far into the future?

Tip: Always ensure the range of your predictions lies within the limits of your data to maintain reliability.