To find the line of best fit for the given data points and determine the value of $b$ (the y-intercept), we'll calculate the linear regression equation $y = mx + b$ using technology. Let me process the data and compute the regression equation. numpy as np from sklearn.linear_model import LinearRegression

Define the data points

x = np.array([-17, -14, -11, -12, -10, -7, -3, -3, -2, 0, 2, 6, 4]).reshape(-1, 1) y = np.array([8, 7, 6, 4, 1, 3, 2, 0, -4, -2, -3, -5, -6])

Perform linear regression

model = LinearRegression() model.fit(x, y)

Extract the y-intercept (b) value

b = model.intercept_ bThe value of $b$ (the y-intercept) for the line of best fit is approximately -2.26.

Would you like a detailed explanation or visualization of the regression process?

Here are 5 follow-up questions related to this problem:

1. What is the slope ($m$) of the line of best fit for this data?
2. How would changing one data point affect the line of best fit?
3. What does the value of $b$ represent in this context?
4. How can we calculate the correlation coefficient to determine the strength of the linear fit?
5. How would the line of best fit change if the dataset was larger or contained outliers?

Tip: Always check the residuals of the regression to assess how well the model fits the data!