The following table shows the quantity supplied for a commodity with the corresponding price values: X Y 8 10 7 8 3 2 5 6 7 9 Determine the type of correlation that exists between these two.

Based on the data provided, it appears that as the price of the commodity increases, the quantity supplied also increases. This indicates a positive correlation between price and quantity supplied.

Step 1: Calculate the correlation coefficient

The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It can range from -1 to 1, where:

- r = -1 indicates a perfect negative correlation (as one variable increases, the other decreases by a constant amount)
- r = 0 indicates no linear correlation
- r = 1 indicates a perfect positive correlation (as one variable increases, the other increases by a constant amount)

The equation for the correlation coefficient is:

```
r = (n - Σ(xy) - Σx - Σy) / √(n - Σ(x²) - (Σx)²) - √(n - Σ(y²) - (Σy)²)
```

where:

- n is the number of data points
- x is the value of the independent variable (price)
- y is the value of the dependent variable (quantity supplied)
- Σ is the sum of the values

Using the data in the table, we can calculate the correlation coefficient as follows:

```
n = 5
Σx = 8 + 7 + 3 + 5 + 7 = 30
Σy = 10 + 8 + 2 + 6 + 9 = 35
Σxy = 80 + 56 + 6 + 30 + 63 = 235
Σx² = 64 + 49 + 9 + 25 + 49 = 196
Σy² = 100 + 64 + 4 + 36 + 81 = 285

r = (5 - 235 - 30 - 35) / √(5 - 196 - 30²) - √(5 - 285 - 35²)
r = 0.947

```

Step 2: Determine the type of correlation

The calculated correlation coefficient, r = 0.947, is positive and close to 1. This indicates a strong positive linear correlation between price and quantity supplied. This means that as the price of the commodity increases, the quantity supplied also tends to increase, and vice versa.