QUESTIONYour Assignment: Coffee Shop PricesChoosing a ModelYou are helping your boss, the owner of a coffee shop, set prices. She has gathered some data by counting the number of cups sold per day at various prices. Your job is to see if there is a relationship between price and sales for one of the two most popular drinks.Coffee sales:Price: 1.50 2.20 2.70 2.50 2.90 2.00 1.60 2.10 3.00 1.80Sales: 96 79 70 73 64 85 94 83 63 91Tea sales:Price: 2.40 1.50 1.10 1.60 2.50 1.30 1.00 1.70 2.20 2.00Sales: 64 85 94 83 63 91 96 79 70 731. Which drink did you select? Circle one.CoffeeTeaFind a line of best fit.2. Enter the data into your calculator and perform a linear regression. Round a and b to the nearest tenth. (2 points: 1 point for slope and 1 point for y-value of y-intercept)What is your linear regression equation?3. What is the meaning of the slope? (2 points)4. Create a scatterplot for your beverage using the data from the table. Then graph the linear regression equation you found in question 2. (4 points)5. Does the line of best fit seem like a good model for the data? Why or why not? (2 points)6. Complete the table. (10 points: 1 point for each row)Identify the actual number of sales at each price.Use your line of best fit to calculate the predicted sales at each price.PROMPTOn-screen text:Coffee Shop PricesA Begin button starts the animation.[Click "Begin."]On-screen text:You are helping your boss, the owner of a coffee shop, set prices. She has gathered some data by counting the number of cups sold per day at various prices. Your job is to see if there is a relationship between price and sales for one of the two most popular drinks. Will you choose coffee or tea?Which will you choose?[Two images of mugs are shown: one filled with coffee and surrounded by coffee beans, and the other filled with tea, with a sprig of mint next to the mug.][Click "Coffee."] Great! You will look at coffee sales. Use the data in the table to find the line of best fit. Then evaluate your model.[A table with two sets of data is shown.]Price: 1.50, 2.20, 2.70, 2.50, 2.90, 2.00, 1.60, 2.10, 3.00, 1.80Sales: 96, 79, 70, 73, 64, 85, 94, 83, 63, 91[Click "Tea."] Great! You will look at tea sales. Use the data in the table to find the line of best fit. Then evaluate your model.[A table with two sets of data is shown.]Price: 2.40, 1.50, 1.10, 1.60, 2.50, 1.30, 1.00, 1.70, 2.20, 2.00Sales: 64, 85, 94, 83, 63, 91, 96, 79, 70, 73
Accepted Solution
A:
1. For this type of problem you can choose anything you want and the process will still be the same. For the purposes of this answer let us choose coffee as the drink that we are going to analyze.
2. We can find the equation of the line of best fit by inputting the data given in the problem on a calculator/software. For this item I chose to use SPSS. Inputting the data to the software, we get the value of the slope at -22.7 and the y-intercept at 130.3.
EQUATION: [tex]y=-22.7x+130.3[/tex] In this equation x is the price and y represents the sales.
3. The slope tells us how many units the sales would change if we were to increase the price by 1 unit. Since our slope is -22.7, this will tell us that we would see a decrease of 22.7 in sales if we were to increase our price by 1 unit.
4. I have attached the graph as an image below. The scatter plot contained all points from the data that has been given. The line of best fit from the equation calculated in question #2 is also shown in the graph.
5. As we can see, the line of best fit hits all the points in the scatterplot. The other points fall closely from the line. Therefore, we can say that the line of best fit is a good model of the data. For added evidence, we can also compute for the Pearson correlation coefficient which gives us -0.998. This indicates a strong negative relationship.
6. For this item we will just need the equation for the line of best fit and the data that has been given in the problem. For the actual sales, we will just refer to the given while we will compute for the predicted sales using the line of best fit.