To calculate $R^2$ (the coefficient of determination), we need to follow these steps:

1. Understand the Data

You provided the following pairs of data points $(x, y)$:

$x$	$y$
-14.00	1.00
19.20	10.00
45.10	40.00
65.70	100.00
104.00	400.00
125.60	760.00

2. Fit a Linear Regression Model

We will fit a simple linear regression model of the form: $y = \beta_0 + \beta_1 x$ Here, $\beta_0$ is the intercept and $\beta_1$ is the slope.

3. Calculate $R^2$

The $R^2$ value is calculated as: $R^2 = 1 - \frac{SS_{\text{res}}}{SS_{\text{tot}}}$ Where:

• $SS_{\text{res}}$ is the residual sum of squares (the difference between the observed values and the predicted values).
• $SS_{\text{tot}}$ is the total sum of squares (the difference between the observed values and the mean of the observed data).

Let's compute the linear regression model and find $R^2$.The $R^2$ value for the given data set is approximately 0.781. This means that around 78.1% of the variance in the $y$-values is explained by the linear regression model.

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. How do you interpret $R^2$ in regression analysis?
2. What would a perfect $R^2$ score of 1 indicate about the model?
3. How does adding more data points affect the $R^2$ value?
4. What is the difference between $R^2$ and adjusted $R^2$?
5. How do we check if a linear model is the best fit for the data?

Tip: If $R^2$ is low, consider using a polynomial or another type of regression model for better fitting.