Question

getting started frozen yogurt... when its freezing? a schools club for aspiring business leaders is helping a local frozen yogurt shop analyze how the business is affected by the weather. the owner is wondering whether there is a relationship between the temperature and the number of customers that buy yogurt during the 2 hours immediately after school. the schools club collected these data. 1. construct a scatter - plot of the collected data. a. plot the first data point. is there a pattern? use a piece of spaghetti to approximate a line that models the data. b. add the second data point to the graph. is there a pattern? adjust the piece of spaghetti to approximate a line that models the data with the additional point. c. add the third data point to the graph. describe the pattern that you see. approximate the line using the spaghetti. d. continue this process until all five data points are plotted and recorded in the table. 2. use your linear model to describe the relationship between the temperature outside and the number of customers at the frozen yogurt shop.

Explanation:

Step1: Construct scatter - plot

Plot each pair of (Temperature, Number of Customers) as points on the graph. For example, for the first data point (45, 97), find 45 on the x - axis (Temperature) and 97 on the y - axis (Number of Customers) and mark the point.

Step2: Analyze patterns

As we add points one by one, observe if the points seem to cluster around a certain shape. Initially, with one point, there is no pattern. As more points are added, we can see if they form a linear or non - linear pattern.

Step3: Approximate line

Use a piece of spaghetti to fit a line that seems to pass through or near most of the points. This is a visual way to estimate a linear model.

Step4: Describe relationship

If the points form a linear pattern, we can say if the relationship is positive (as temperature increases, number of customers increases) or negative (as temperature increases, number of customers decreases).

Answer:

1. Follow the steps above to construct the scatter - plot, analyze patterns, approximate the line, and describe the relationship. For the linear model in part 2, if the line has a positive slope, it means as the temperature outside increases, the number of customers at the frozen yogurt shop increases. If the slope is negative, as the temperature outside increases, the number of customers decreases. Without actually performing the graphical operations, we can't give a specific numerical relationship or exact description of the pattern, but the general process is as described.