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
Referring to the table, what is the estimated average change in the sales of the candy bar if price goes up by $1.00?
A) 161.386
B) 0.784
C) -3.810
D) -48.193
Referring to the table, what is the coefficient of correlation for these data?
A) -0.8854
B) -0.7839
C) 0.7839
D) 0.8854

Answer 1

-48.193

-48.193

-0.8854

Step-by-step explanation:

Given the data:

Price (X) : 1.30, 1.60, 1.80, 2.00, 2.40, 2.90

Sales (Y) : 100, 90, 90, 40, 38, 32

To answer the questions, we create a linear regression equation, using an online regression calculator :

The regression model obtained is :

ŷ = -48.1928X + 161.3855

The general form of a regression equation is :

y = mx + c

Where ;

y = dependent variable ; x = independent variable ; m = slope ; c = intercept

From the model, slope, m = - 48.1928

2.) Estimated average change if price goes up by $1.00

This is the value of the slope which is the average rate of Change in the dependent variable if the independent variable charges by 1 unit.

= - 48.193

C.)

Coefficient of correlation : - 0.8854 (using the correlation Coefficient calculator) ; This implies a strong negative correlation between the variables.