To find the equation of the least-squares regression line and calculate the residuals, we need the following:

1. Equation of the least-squares regression line:
   The formula is $\hat{y} = b_0 + b_1 x$, where:

   • $b_1 = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sum (x_i - \bar{x})^2}$ is the slope,
   • $b_0 = \bar{y} - b_1 \bar{x}$ is the intercept.

2. Residuals:
   A residual for each data point is calculated as: $\text{Residual} = y_i - \hat{y}_i$ where $y_i$ is the actual value and $\hat{y}_i$ is the predicted value from the regression line.

To proceed, I'll need the corresponding $y$-values (dependent variable) for the given $x$-values: $4.0, 7.0, 10.0, 13.5, 17.0$. Can you provide the $y$-values, or should I assume them to calculate the regression line and residuals?

Let me know if you want more details or have any specific questions! Here are some questions to deepen your understanding:

1. What is the significance of the least-squares regression line?
2. How is the slope of the regression line interpreted in real-world contexts?
3. Why do we calculate residuals in regression analysis?
4. What happens when residuals are large?
5. How can the residual plot help in diagnosing model fit?

Tip: Always visualize the regression line and residuals to get better insights into the model's accuracy!