Question

100 points if correct In this task, you will play the role of a restaurant owner. You will collect data and analyze different aspects of your business.

As you complete the task, keep these questions in mind: Can you predict sales based on factors such as the weather and the number of customers? Can you estimate the amount you will earn in tips on a given day based on the number of customers?
Directions:
Complete each of the following tasks, reading the directions carefully as you go. You may use a piece of graph paper for this task.
Round all decimals to the nearest hundredths place or to the nearest cent for this task.
You will be graded on the work you show, or your solution process, in addition to your answers. Make sure to show all of your work and to answer each question as you complete the task. You will be given partial credit based on the work you show and the completeness and accuracy of your explanations.
Your teacher will give you further directions on submitting your work. You may be asked to upload the document, e-mail it to your teacher, or hand in a hard copy.
Now let’s get started!


Step 1: Constructing and analyzing scatterplots


You keep track of the daily hot chocolate sales and the outside temperature each day. The data you gathered is shown in the data table below.

Hot Chocolate Sales and Outside Temperatures
Sales ($) $100 $213 $830 $679 $209 $189 $1,110 $456 $422 $235 $199
Temperature (°F) 92° 88° 54° 62° 85° 16° 52° 65° 68° 89° 91°

a) Make a scatterplot of the data above. (2 points)

b) Do you notice clusters or outliers in the data? Explain your reasoning. (2 points)








c) How would you describe the correlation in the data? Explain your reasoning. (2 points)








d) What are the independent and dependent variables? (2 points)








Step 2: Evaluating trends of data

Because you want to prepare and serve the healthiest food possible, you monitor the fat and calorie content of items on your menu. Some of the menu items are included in the graph below.



a) Your business partner describes this as a high positive correlation. Is your partner correct? Why or why not? (2 points)






b) Using the drawing tools, draw a trend line (line of best fit) on the graph above. (2 points)




c) Judge the closeness of your trend line to the data points. Do you notice a relationship between the data points? (2 points)






d) Is the trend line linear? If so, write a linear equation that represents the trend line. Show your work. (3 points)










Step 3: Making predictions using data

You and your business partner track the number of customers served and the amount of tips collected per day. The data you gathered is displayed in the chart below.

Servers’ Collected Tips
Customers 54 46 34 67 52 22 49 64 55 80 38 42
Tips ($) $92 $80 $76 $121 $109 $43 $87 $114 $99 $174 $88 $91

a) Create a scatterplot displaying the data in the table. Be sure to include a linear trend line. (2 points)







b) Find the equation of the trend line (line of best fit). Show your work. (2 points)



















c) Predict the amount of tips that would be collected if 100 customers were served at the restaurant on a given day. Explain your reasoning. (2 points)


d) Explain how to use the regression calculator to make a reasonable prediction given a data table. (2 points)

Answer 1

a) Make a scatterplot of the data above. b) Do you notice clusters or outliers in the data? Explain your reasoning. c) How would you describe the correlation in the data? Explain your reasoning.

Step-by-step explanation:

a. Make a scatterplot of the data above:

1. Plot the temperature (in °F) on the x-axis and the hot chocolate sales (in $) on the y-axis.
2. For each data point, plot a dot at the corresponding temperature and sales value.
3. Connect the dots to create a scatterplot.

b. Do you notice clusters or outliers in the data? Explain your reasoning:

From the scatterplot, it appears that there is no clustering or outliers in the data. The data points are scattered evenly around the plot without any distinct patterns or groups.

c. How would you describe the correlation in the data? Explain your reasoning:

Based on the scatterplot, there doesn't seem to be a strong correlation between the temperature and hot chocolate sales. The data points are randomly scattered across the plot, indicating that there is no clear relationship between the two variables.

d. What are the independent and dependent variables?

The independent variable in this scenario is the outside temperature. The dependent variable is the hot chocolate sales, which is influenced by the temperature.