Question

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:

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

Referring to the above listed table, what is the estimated slope parameter for the candy bar price and sales data?

(A) 161.386
(B) 0.784
(C) -3.810
(D) -48.193

Answer 1

(D) -48.193

Explanation:

We know that regression equation is

y=a+bx where a is intercept and b is slope of the regression equation.

`Slope=b=(sum(x-xbar)(y-ybar))/(sum(x-xbar)^2)`

City Price ($)(x) Sales(Y)

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

xbar=sumx/n=12/6=2

ybar=sumy/n=390/6=65

x y x-xbar y-ybar (x-xbar)(y-ybar) (x-xbar)²

1.3 100 -0.7 35 -24.5 0.49

1.6 90 -0.4 25 -10 0.16

1.8 90 -0.2 25 -5 0.04

2 40 0 -25 0 0

2.4 38 0.4 -27 -10.8 0.16

2.9 32 0.9 -33 -29.7 0.81

Total -80 1.66

`Slope=b=(sum(x-xbar)(y-ybar))/(sum(x-xbar)^2)`

b=-80/1.66

b=-48.193