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:

CityPrice (S)Sales River Falls.010 Hudson Ellsworth Prescott Rock Elnm Stillwater 1.60 1.80 2.00 2.40 2.90 100 90 90 40 38 32

using the above table, answer the following questions:

1. Referring to the above Table , what is the estimated slope parameter for the candy bar price and sales data?

2. Referring to the above Table, what is the estimated average change in the sales of the candy bar if price goes up by $1.00?

3. Referring to Table, what is the coefficient of correlation for these data?

4. Referring to Table , what is the percentage of the total variation in candy bar sales explained by the regression model?

5. Referring to Table , what percentage of the total variation in candy bar sales is explained by prices?

Answer 1

	Price	Sales	p^2	S^2	P*S
	1.3	100	1.69	10000	130
	1.6	90	2.56	8100	144
	1.8	90	3.24	8100	162
	2	40	4	1600	80
	2.4	38	5.76	1444	91.2
	2.9	32	8.41	1024	92.8
Sum	12	390	25.66	30268	700
Mean	2	65
N	6

1) Y'=a+bX

Slope: $b=\frac{N\sum XY-(\sum X)(\sum Y)}{N\sum X^2-(\sum X)^2}=-48.192771$

2)

X=1

$Y'=161.3855422-48.192771*1=113.1928$

3)Correlation coefficient:

$r=\frac{N\sum XY-(\sum X)(\sum Y)}{\sqrt{[N\sum X^2-(\sum X)^2][N\sum Y^2-(\sum Y)^2]}}=-0.8854044$

4) Total percentage of variation explained by regression model:

Coefficient of determination-R-squared: $r^2=-0.8854044^2=0.78394097$ =78.394097%