Question

please show your work.

A candy bar manufacturer is interested in trying to estimate how sales are influenced by

the price of their product. To do this, the company randomly chooses 6 small cities and

offers the candy bar at different prices. Using candy bar sales as the dependent variable,

the company will conduct a simple linear regression on the data below: [20 points]

City Price ($) Sales

River Falls 1.30 100

Hudson 1.60 90

Ellsworth 1.80 90

Prescott 2.00 40

Rock Elm 2.40 38

Stillwater 2.90 32

   (a) Set up a scatter diagram.

   (b) Assuming a linear relationship, use the least-squares method to find the regression

coefficients bo and b1.

(c) Interpret the meaning of the slope b1 in this problem.

(d) Predict the sales when the prices are $1.50 and $2.70.

Answer 1

Answer a)

Scatter plot is as follows:

Answer b)

Regression coefficient are b0 = 161.386 and b1 = -48.193

Answer c)

The value of b1 is negative. It shows that increase in price reduces the candy sales. The magnitude of b1 is -48.193 meaning $1 increase in price reduces the candy sales by 48.193 units.

Answer d)

At x = $1.50

y = 161.386 − 48.193*1.50

y = 89.0965

At x = $2.70

y = 161.386 − 48.193*2.70

y = 31.2649