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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
For these data:
1. Determine the regression coefficients 0 and 1.
2. What is the coefficient of correlation for these data?
3. What is the percentage of the total variation in candy bar sales explained by prices?
4. What is the standard error of the estimate, SYX, for the data?
5. At the 0.01 level of significance, is there evidence of a linear relationship between the sales and the prices?

Answer :

Fichohgo

Using technology, the linear equation which models the relationship between price and sales can be represented thus : y = -48.2x + 161.4

The solution to the remaining problems are provided thus :

2.)

The Correlation Coefficient,R is the measure of the strength and direction of the association between the variables. Hence, R = - 0.885

3.)

The percentage of explained variance is given by the coefficient of determination,R² hence, the R² value is 0.784. Hence, about 78.4% of candy bar sales is explained by price.

4.)

The Pvalue = 0.0189

α = 0.01

Since, Pvalue > α ; we fail to reject H0. Hence, there is no evidence of a relationship between sales and price.

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