Final answer:
The relationship between ice cream sales and temperature is typically modeled using a simple linear equation y = mx + b. The y-intercept b is the predicted sales at 0 degrees Celsius, while the slope m indicates how much sales increase per degree. To estimate sales at a certain temperature, plug that temperature into the equation as x and solve for y.
Step-by-step explanation:
Understanding the Relationship Between Ice Cream Sales and Temperature
When attempting to understand the relationship between variables such as ice cream sales and temperature, we use the method of regression analysis to derive a linear equation. This equation can help us predict one variable based on the known values of another. The linear relationship is often written in the form y = mx + b, where m represents the slope of the line, and b is the y-intercept.
To answer your questions:
- The y-intercept is the value of y when x is zero. For the ice cream sales scenario, this would represent the baseline number of ice cream cones sold at a temperature of 0 degrees Celsius.
- The slope is a measure of how much y changes for a one-unit change in x. It represents the increase in sales per degree rise in temperature.
- To predict the expected number of cones sold at 18 degrees Celsius, you would substitute 18 for x in the equation and solve for y.
In our example, if the y-intercept is given as 9 (from the reference info), and the slope of the line is said to be 3, then our linear model would be y = 3x + 9. To predict the sales at 18 degrees Celsius, we substitute 18 for x giving us y = 3(18) + 9 = 54 + 9 = 63. Therefore, we would expect 63 cones of ice cream to be sold at 18 degrees Celsius.