Question

A small independent organic food store offers a variety of specialty coffees. To determine whether price has an impact on sales, the managers kept track of how many pounds of each variety of coffee were sold last month. Based on the data and summary statistics shown below, the slope of the estimated regression line that relates the response variable (monthly sales) to the predictor variable (price per pound) is
PRICE PER POUND POUNDS SOLD

$ 3.99 75

$ 5.99 60

$ 7.00 65

$ 12.00 45

$ 4.50 80

$ 7.50 70

$ 15.00 25

$ 10.00 35

$ 12.50 40

$ 8.99 50



Mean $ 8.75 54.50
Standard Deviation $ 3.63 18.33
Correlation -0.927
Question 2 options:
-4.681.
-0.858.
0.858.
-8.999.
95.459

Answer 1

Answer:

b= -4.68

Step-by-step explanation:

Hello!

We have to study variables:

Y: Monthly coffe sales

X: Price per pound of coffe ($)

The estimate regression line is

^Yi= a + bxi ∀ (i=1,.....,10)

The slope of the estimated regression line is represented by b.

The formula I'll use to calculate it is:

b= [n∑xiyi -(∑xi)*(∑yi)]/ n∑xi²-(∑xi)²

To calculate b we need to do some auxiliary calculations:

∑xiyi= 4213.15

∑xi= 87.47

∑yi= 545

∑xi²= 883.3703

Then we replace the formula:

b= [10*4213.15-(87.47)*(545)]/ n883.3703-(87.47)²

b= -4.68

I hope you have a SUPER day!