To analyze the situation described, we need to utilize the equation of the regression line, which typically has the form:
\[ y = mx + b \]
Where:
- \( y \) is the predicted number of customers.
- \( x \) is the number of flyers distributed.
- \( m \) is the slope of the line (the change in the number of customers for each additional flyer).
- \( b \) is the y-intercept (the predicted number of customers when no flyers are distributed, i.e., when \( x = 0 \)).
1. Predicting the number of customers when zero flyers are distributed
To find out how many people would visit the shop if zero flyers were distributed, we need to evaluate the regression line at \( x = 0 \):
\[ y = m(0) + b \] \[ y = b \]
The value of \( b \) (the y-intercept) will give us the estimated number of customers when no flyers are distributed.
2. Effect of one additional flyer on the number of customers
The slope \( m \) of the regression line indicates how much the number of customers increases for each additional flyer. Therefore, if one additional flyer is distributed, the number of customers is predicted to increase by \( m \).
3. Predicting the number of customers for 100 flyers
To calculate how many people are expected to visit the shop if 100 flyers are distributed, we substitute \( x = 100 \) into the regression equation:
\[ y = m(100) + b \]
This will provide the average number of customers expected when 100 flyers are distributed.
Conclusion
To provide specific numerical answers, the actual values of \( m \) and \( b \) from the regression analysis must be known. However, the process to answer the questions is as follows:
- The number of customers with zero flyers is \( b \).
- The increase in customers from one additional flyer is \( m \).
- The estimated customers with 100 flyers is \( 100m + b \).
If you have the values for \( m \) and \( b \), you can plug them into this formula for concrete answers.