To write the estimated regression equation using the least squares estimates, we need to determine the estimates for $b_0$ and $b_1$. These estimates represent the y-intercept and the slope of the regression line, respectively.

The general form of the simple linear regression equation is:

$\hat{y} = b_0 + b_1x$

Where:

• $\hat{y}$ is the predicted value of the dependent variable.
• $b_0$ is the y-intercept (the value of $\hat{y}$ when $x = 0$).
• $b_1$ is the slope of the regression line (the change in $\hat{y}$ for a one-unit change in $x$).
• $x$ is the independent variable.

Step 1: Compute $b_1$ (the slope)

The formula for $b_1$ is: $b_1 = \frac{\sum{(x_i - \bar{x})(y_i - \bar{y})}}{\sum{(x_i - \bar{x})^2}}$

Step 2: Compute $b_0$ (the y-intercept)

The formula for $b_0$ is: $b_0 = \bar{y} - b_1\bar{x}$ Where:

• $\bar{x}$ is the mean of the independent variable $x$.
• $\bar{y}$ is the mean of the dependent variable $y$.

Step 3: Write the Regression Equation

Once $b_0$ and $b_1$ are calculated, substitute them into the regression equation:

$\hat{y} = b_0 + b_1x$

Since the specific values for $x_i$ and $y_i$ are not provided in your question, I cannot calculate the exact estimates for $b_0$ and $b_1$. However, if you provide the data points or summary statistics (like means and sums), I can compute these values for you and write the final estimated regression equation.

Would you like to provide the data or further details?

---

Next Steps:

1. What are $x_i$ and $y_i$ data points?
2. How is $b_1$ calculated?
3. How is $b_0$ calculated?
4. What is the significance of $b_1$ in regression?
5. How do you interpret the regression equation?
6. What happens if $b_1$ is negative?
7. Can you calculate the regression equation with given summary statistics?
8. How does the least squares method minimize errors?

Tip: Always check your data for outliers, as they can significantly impact the regression results.