find R squared from this set of data points:-14.00	1.00
19.20	10.00
45.10	40.00
65.70	100.00
104.00	400.00
125.60	760.00

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.

find R squared from this set of data points:-14.00 1.00 19.20 10.00 45.10 40.00 65.70 100.00 104.00 400.00 125.60 760.00

Learn how to calculate R-Squared (R^2) for a given set of data points using linear regression. This problem covers key statistical concepts, such as the coefficient of determination and least squares regression. Suitable for students in Grades 10-12 or early college level.

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