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To solve the problem of fitting a straight line using the method of least squares, we follow these steps:

### Step 1: General form of the straight line
The equation of the straight line is given by:
\[
y = mx + c
\]
where \(m\) is the slope and \(c\) is the y-intercept.

### Step 2: Calculate necessary summations
We need the following values from the data for \(x\) and \(y\):

| \(x\) | \(y\) |
|------|------|
| 0    | 2    |
| 1    | 3    |
| 2    | 5    |
| 3    | 7    |
| 4    | 9    |
| 5    | 15   |

The summations required are:
- \( \sum x \)
- \( \sum y \)
- \( \sum x^2 \)
- \( \sum xy \)

I'll calculate these summations now.The calculated summations are:

\[
\sum x = 15, \quad \sum y = 41, \quad \sum x^2 = 55, \quad \sum xy = 145
\]

### Step 3: Use the least squares formulas to calculate \(m\) and \(c\)
The formulas for slope (\(m\)) and y-intercept (\(c\)) are:

\[
m = \frac{n \sum xy - \sum x \sum y}{n \sum x^2 - (\sum x)^2}
\]
\[
c = \frac{\sum y \sum x^2 - \sum x \sum xy}{n \sum x^2 - (\sum x)^2}
\]

I'll compute \(m\) and \(c\) now.The equation of the straight line fitted using the method of least squares is:

\[
y = 2.43x + 0.76
\]

Would you like more details or further explanation on how this was derived?

Here are five related questions you might find helpful:
1. How can I plot this straight line along with the given data points?
2. What is the interpretation of the slope and y-intercept in this context?
3. How would the least squares method change for non-linear data?
4. What are the assumptions behind using the least squares method?
5. Can you show the step-by-step derivation of the least squares formulas?

**Tip:** The least squares method minimizes the sum of the squared vertical distances between the observed points and the fitted line.

Fit a straight line for the following data by the method of least squares: x = [0, 1, 2, 3, 4, 5], y = [2, 3, 5, 7, 9, 15]

Learn how to fit a straight line using the least squares method for the data points x = [0, 1, 2, 3, 4, 5] and y = [2, 3, 5, 7, 9, 15]. This problem involves linear regression concepts, algebraic summations, and the least squares formula. Suitable for students in Grades 9-12.

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