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. Identify the Data Points
   We have the following data from the table:

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

2. Calculate the Slope (m) of the Linear Function
   Using two points from the data, we can calculate the slope $m$ using the formula: $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
   For example, using points (629, 38) and (914, 53): $$ m = \frac{53 - 38}{914 - 629} = \frac{15}{285} \approx 0.0526 $$

3. Use the Point-Slope Form to Find the Linear Equation
   Now we can use point-slope form $y - y_1 = m(x - x_1)$ with one of the points, let's say (629, 38): $$ y - 38 = 0.0526(x - 629) $$ Rearranging gives: $$ y = 0.0526x + (38 - 0.0526 \times 629) $$

4. Calculate the Y-Intercept
   To find the y-intercept, calculate: $$ b = 38 - (0.0526 \times 629) \approx 38 - 33.06 \approx 4.94 $$ Thus, the linear function is: $$ y = 0.0526x + 4.94 $$

5. Predict the Number of Clicks for 1,500 Visitors
   Now, substitute $x = 1500$ into the equation: $$ y = 0.0526(1500) + 4.94 $$ Calculating gives: $$ y = 78.9 + 4.94 \approx 83.84 $$

6. Round the Number of Clicks
   Rounding the prediction, we can conclude that the predicted number of clicks is approximately 84. The closest option is 83.