The table provided shows a relationship between the number of visits to a website (denoted as $x$) and the number of advertisement clicks (denoted as $y$). To predict the number of clicks if 1,500 people visit the website, we can apply linear regression to estimate the relationship between $x$ and $y$.

Steps to solve:

1. Identify the data points from the table:

   • $(153, 14), (629, 38), (471, 30), (914, 53), (307, 21), (1,045, 60), (510, 32), (1,106, 63)$

2. Fit a linear regression equation in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

3. Use the formula for the slope: $m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$ where $n$ is the number of data points.

4. Calculate the y-intercept using: $b = \frac{\sum y - m(\sum x)}{n}$

5. Substitute $x = 1,500$ into the regression equation to predict $y$.

I'll calculate this and provide the best prediction.Using linear regression, the best prediction for the number of clicks on the advertisement when 1,500 people visit the website is approximately 83. Therefore, the correct answer is:

C. 83

Would you like a detailed breakdown of how the linear regression was calculated, or do you have any questions?

Here are 5 questions to expand on the topic:

1. How does linear regression help in making predictions based on data?
2. What are some limitations of using linear regression for making predictions?
3. How do outliers in data affect the accuracy of a linear regression model?
4. Can we apply this method to predict outcomes in non-linear relationships? How?
5. What are other types of regression techniques besides linear regression?

Tip: Always visualize the data points and the fitted line when applying linear regression to better understand the relationship between variables.