what is the percentage of the total variation in candy bar sales explained by the regression model? a. 78.39% b. 88.54% c. 100% d. 48.19%

Complete 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 City - - 1.30 - - - - - - 100

Hudson - - - 1.60 - - - - - 90

Ellsworth - - - 1.80 - - - - - 90

Prescott - - - - 2.00 - - - - 40

Rock Elm - - 2.40 - - 38

Stillwater - - 2.90 - - 32

78.39%

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

The percentage of the total variation in candy bar sales explained by the regression model can be obtained from the value of the Coefficient of determination(R^2) of the regression model. The Coefficient of determination is a value which ranges between 0 - 1 and gives the proportion of variation in the dependent variable which can be explained by the dependent variable.

R^2 value is obtained by getting the squared value of R(correlation Coefficient).

The R value obtained using the online R value calculator on the data is : - 0.8854

Hence, R^2 = (-0.8854)^2 = 0.7839

Expressing 0.7839 as a percentage ;

0.7839 × 100 = 78.39%