Based on the table, what is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website?

Steps to Solve

1. Set Up the Data Points

Extract the data points from the table for analysis:

• Visits (x): 153, 629, 471, 914, 307, 1045, 510, 1106
• Clicks (y): 14, 38, 30, 53, 21, 60, 32, 63

2. Visual Representation / Create a Scatter Plot

Plot these points to visually inspect the relationship. The visits will be on the x-axis and clicks on the y-axis.

3. Calculate the Linear Regression Equation

Use linear regression to find the best fit line for the data points. This can be calculated using the formula for the slope $m$ and y-intercept $b$ of the line $y = mx + b$.

Step 3.1: Calculate the slope ($m$):

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

Step 3.2: Calculate the y-intercept ($b$):

$$ b = \frac{\sum y - m(\sum x)}{n} $$

Where $n$ is the number of data points.

4. Use the Regression Equation to Predict Clicks

Substitute $x = 1500$ (the number of visits) into the linear regression equation obtained in Step 3.

5. Calculate the Predicted Value

After substituting $x=1500$, calculate the value of $y$ which will give the predicted number of clicks.