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Your Assignment: Coffee Shop Prices

Choosing a Model

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.

Coffee sales:

Price: 1. 50 2. 20 2. 70 2. 50 2. 90 2. 00 1. 60 2. 10 3. 00 1. 80

Sales:

96

79

70

73

64

85

94

83

63

91

Tea sales:

Price: 2. 40 1. 50 1. 10 1. 60 2. 50 1. 30 1. 00 1. 70 2. 20 2. 00

Sales:

64

85

94

83

63

91

96

79

70

73

1. Which drink did you select? Circle one.

Sagot :

MrRoyal

The regression equation of sales of coffee is ŷ = -22.7x + 130.3, and the regression equation of sales of tea is ŷ = -22.7x + 119.0

How to determine the regression equations of the drinks?

The dataset of coffee is given as:

Price: 1.50 2.20 2.70 2.50 2.90 2.00 1.60 2.10 3.00 1.80

Sales: 96 79 70 73 64 85 94 83 63 91

Using a graphing calculator, we have the following calculation summary:

  • Sum of X = 22.3
  • Sum of Y = 798
  • Mean X = 2.23
  • Mean Y = 79.8
  • Sum of squares (SSX) = 2.521
  • Sum of products (SP) = -57.14
  • b = SP/SSX = -57.14/2.52 = -22.7
  • a = MY - bMX = 79.8 - (-22.67*2.23) = 130.3

The regression equation is represented as:

ŷ = bx + a

So, we have:

ŷ = -22.7x + 130.3

The dataset of tea is given as:

Price: 2.40 1.50 1.10 1.60 2.50 1.30 1.00 1.70 2.20 2.00

Sales: 64 85 94 83 63 91 96 79 70 73

Using a graphing calculator, we have the following calculation summary:

  • Sum of X = 17.3
  • Sum of Y = 798
  • Mean X = 1.73
  • Mean Y = 79.8
  • Sum of squares (SSX) = 2.521
  • Sum of products (SP) = -57.14
  • b = SP/SSX = -57.14/2.52 = -22.7
  • a = MY - bMX = 79.8 - (-22.67*1.73) = 119.0

The regression equation is represented as:

ŷ = bx + a

So, we have:

ŷ = -22.7x + 119.0

Hence, the regression equation of sales of coffee is ŷ = -22.7x + 130.3, and the regression equation of sales of tea is ŷ = -22.7x + 119.0

Read more about regression at:

https://brainly.com/question/17844286

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