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 $y$:

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.