To calculate the Pearson correlation coefficient $r$ for the given data, we use the following formula:

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

Where:

• $x$ is the number of TV commercials.
• $y$ is the number of car sales (in hundreds).
• $n$ is the number of data points (in this case, 5).

Let's break this down step-by-step:

Step 1: Organize the data

City	Number of TV commercials, $x$	Car sales $y$ (in hundreds)
1	55	3
2	6	2
3	13	9
4	14	5
5	19	8

Step 2: Calculate the required values

We need to compute the following sums:

1. $\sum x$ — sum of all $x$ values.
2. $\sum y$ — sum of all $y$ values.
3. $\sum x^2$ — sum of all $x^2$ values.
4. $\sum y^2$ — sum of all $y^2$ values.
5. $\sum xy$ — sum of the products of corresponding $x$ and $y$.

$\sum x = 55 + 6 + 13 + 14 + 19 = 107$ $\sum y = 3 + 2 + 9 + 5 + 8 = 27$ $\sum x^2 = 55^2 + 6^2 + 13^2 + 14^2 + 19^2 = 3025 + 36 + 169 + 196 + 361 = 3787$ $\sum y^2 = 3^2 + 2^2 + 9^2 + 5^2 + 8^2 = 9 + 4 + 81 + 25 + 64 = 183$ $\sum xy = (55 \times 3) + (6 \times 2) + (13 \times 9) + (14 \times 5) + (19 \times 8) = 165 + 12 + 117 + 70 + 152 = 516$

Step 3: Apply the Pearson correlation coefficient formula

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

Substitute the