To write the equation of the least-squares regression line, we use the given formula:

$\hat{y} = a + b x$

Where:

• $a = 1.84227408$ (intercept)
• $b = 0.36006575$ (slope)

Substituting these values into the equation:

$\hat{y} = 1.84227408 + 0.36006575x$

This is the equation of the regression line.

Would you like an explanation of how the regression line is used or further clarification?

Related Questions:

1. What is the significance of the slope ($b$) in the regression line?
2. How does the correlation coefficient ($r$) relate to the $r^2$ value?
3. What does the $r^2$ value of 0.453994123 indicate about the model's accuracy?
4. Can the regression equation predict values outside the given data range?
5. How do you interpret the intercept ($a$) in a real-world scenario?

Tip:

Always check the $r^2$ value (coefficient of determination) to understand how well the regression model fits the data. A higher $r^2$ indicates a better fit.