100 points!!!! and brainliest!!!!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.
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.
d) What are the independent and dependent variables?
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
b) Using the drawing tools, draw a trend line (line of best fit) on the graph above.
c) Judge the closeness of your trend line to the data points. Do you notice a relationship between the data points?
d) Is the trend line linear? If so, write a linear equation that represents the trend line. Show your work.
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.
b) Find the equation of the trend line (line of best fit). Show your work.
c) Predict the amount of tips that would be collected if 100 customers were served at the restaurant on a given day.
d) Explain how to use the regression calculator to make a reasonable prediction given a data table.

Answer:

step 1

b) Yes,I do 1,110 is a cluster because it’s a very large number for 52 degrees and 189 is because it’s a very large number for 16 degrees.

c) There is a negative correlation.

d) The dependent variable is sales and independent variable is the temperature.

step 2

a) yes my partner is correct because the line goes diagonally upwards.

b) The trend line lies on the points (0,100) and (15,900)D .

c) Yes I do see a relationship. This line move one direction up. notice how the dots move up like an escalator

d) Yes do see a relationship. This line move one direction up. notice how the dots move up like an escalator.

step 3

b) 1.875x+12.25

c) 50

d) Given data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.  

1)Enter data into the regression calculator.

2)Determine the regression equation.

3)Substitute the correct value for x or y into the equation.

4)Simplify to find the value of the other variable.

(1,2,3,4, goes with step 3 D)

Step-by-step explanation:

Final answer:

This question involves scatterplots, correlations, identifying independent and dependent variables, trend lines, and making predictions through data analysis and regression.

Explanation:

This question requires a detailed understanding of data analysis, including scatterplots, correlation, trend lines, and regression. First, to make a scatterplot of the hot chocolate sales and outside temperatures, you would plot each pair of data points with the temperature on the x-axis and the sales on the y-axis. Detecting clusters or outliers would require inspecting the graph and watching for data points that stray far from the others. The correlation could be negative, as lower temperatures seem to correspond with higher sales.

The independent variable is the outside temperature, and the dependent variable is the hot chocolate sales. In the next part, a high positive correlation indicates that as the fat content increases, so does the calorie content. The trend line in this graph likely goes upwards when drawn. If it fits closely to the data points, then there is a strong positive correlation.

In the third part, you'd want to plot the number of customers against the amount of tips received to identify the trend. Using this trend line, you could then predict potential earnings given a certain number of customers. A regression calculator could be used to define precise relationships in the data and make accurate predictions.

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