Based on the table, what is the best prediction of the number of clicks on the advertisement if 1,500 people visit the website?
Understand the Problem
The question is asking to predict the number of clicks on an advertisement based on the data given in the table when 1,500 people visit the website. It requires analyzing the relationship between the number of website visits and advertisement clicks using a linear function.
Answer
$83$
Answer for screen readers
The best prediction of the number of clicks on the advertisement if 1,500 people visit the website is $83$.
Steps to Solve
-
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)
-
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): $$ m = \frac{53 - 38}{914 - 629} = \frac{15}{285} \approx 0.0526 $$ -
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: $$ y = 0.0526x + (38 - 0.0526 \times 629) $$ -
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: $$ y = 0.0526x + 4.94 $$ -
Predict the Number of Clicks for 1,500 Visitors
Now, substitute $x = 1500$ into the equation: $$ y = 0.0526(1500) + 4.94 $$ Calculating gives: $$ y = 78.9 + 4.94 \approx 83.84 $$ -
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.
The best prediction of the number of clicks on the advertisement if 1,500 people visit the website is $83$.
More Information
This prediction uses linear regression to analyze the relationship between website visits and advertisement clicks. The prediction method is applicable in advertising and marketing analytics.
Tips
- Failing to choose appropriate data points for calculating the slope. Ensure to select points that represent the range well.
- Miscalculating the slope or y-intercept. Double-check math steps.
- Not rounding properly or misunderstanding how to interpret the closest answer option.