To find the regression line (or the line of best fit) for the given data points, we use the formula for a simple linear regression:

$y = mx + b$

Where:

• $m$ is the slope of the line
• $b$ is the y-intercept

Step 1: Organize the data

Step 2: Compute required values

We calculate:

1. $\sum X$ (sum of $X$-values)
2. $\sum Y$ (sum of $Y$-values)
3. $\sum XY$ (sum of the product of corresponding $X$ and $Y$-values)
4. $\sum X^2$ (sum of squares of $X$-values)
5. Number of points ($n$).

$\text{Sum } (\sum X = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28)$ $\text{Sum } (\sum Y = 1.5 + 3.8 + 6.7 + 9.0 + 11.2 + 13.6 + 16.0 = 61.8)$ $\text{Sum } (\sum XY = 1 \cdot 1.5 + 2 \cdot 3.8 + 3 \cdot 6.7 + 4 \cdot 9.0 + 5 \cdot 11.2 + 6 \cdot 13.6 + 7 \cdot 16.0 = 301.6)$ $\text{Sum } (\sum X^2 = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 = 140)$ $n = 7$

Step 3: Compute the slope ($m$) and intercept ($b$)

The formulas are: $m = \frac{n \sum XY - \sum X \sum Y}{n \sum X^2 - (\sum X)^2}$ $b = \frac{\sum Y - m \sum X}{n}$

Substitute the values: