The table below shows the size (in carats) and the price (in rands) of 10 diamonds that were sold by a diamond trader - NSC Mathematics - Question 2 - 2022 - Paper 2

To find the least squares regression line, we need to calculate the slope (m) and the y-intercept (b) using the least squares formula. The linear regression formula is given by:

$y = mx + b$

Where:

• $m = \frac{N(\sum xy) - (\sum x)(\sum y)}{N(\sum x^2) - (\sum x)^2}$
• $b = \frac{\sum y - m (\sum x)}{N}$

1. Calculate the summations:

   • $\sum x = 0 + 0.15 + 0.2 + 0.25 + 0.3 + 0.35 + 0.4 + 0.45 + 0.5 + 0.55 = 3.00$
   • $\sum y = 4000 + 6000 + 5800 + 9000 + 10440 + 12160 + 15120 + 18480 = 104000$
   • $\sum xy = (0 * 4000) + (0.15 * 6000) + (0.2 * 5800) + (0.25 * 9000) + (0.3 * 10440) + (0.35 * 12160) + (0.4 * 15120) + (0.45 * 18480) = 52090$
   • $\sum x^2 = 0^2 + 0.15^2 + 0.2^2 + 0.25^2 + 0.3^2 + 0.35^2 + 0.4^2 + 0.45^2 + 0.5^2 + 0.55^2 = 0.385625$
   • $N = 10$ (number of data points)

2. Substitute these values into the formulas for $m$ and $b$ to determine the equation.

This results in the least squares regression equation being:

$y = mx + b$