To find the line of best fit for the given data using linear regression, we can follow these steps:

1. Identify the Data Points:

The data pairs $(w, k(w))$ are as follows: $(1, 724), (2, 697), (3, 764), (4, 757), (5, 803), (6, 818)$

2. Use the Linear Regression Formula:

The line of best fit is typically of the form: $k(w) = mw + b$ where $m$ is the slope and $b$ is the y-intercept.

3. Calculate Using a Graphing Calculator or Software:

Using a graphing calculator or software (like Excel, Google Sheets, or a statistical calculator), input the data to perform linear regression, which will yield the values of $m$ and $b$.

I'll compute the linear regression for you now.The line of best fit for the given data is:

$k(w) = 22.314w + 682.400$

This equation is rounded to three decimal places as requested.

Would you like more details or have any further questions? Here are some related questions that might interest you:

1. How can you calculate the correlation coefficient from the regression analysis?
2. What does the slope of the line represent in the context of this data?
3. How can you use this linear equation to predict $k(w)$ for a given value of $w$?
4. What is the significance of the y-intercept in this linear regression?
5. How would the equation change if an outlier was added to the dataset?

Tip: To check the accuracy of your linear regression model, you can calculate the residuals (differences between observed and predicted values) and analyze their distribution.