Question

3. A candy bar manufacturer is interested in estimating sales using price of the candy bar in different cities. To do this the manufacturer randomly selected 6 small cities and offered the candy at different price. Using candy bar sales as dependent variable, the manufacturer will conduct simple regression using the data below:

Price (X) Sales (Y) XY X² Y²

1.3 100 130 1.69 10000

1.6 90 144 2.56 8100

1.8 90 162 3.24 8100

2 40 80 4 1600

2.4 38 91.2 5.76 1444

3.5 20 70 12.25 400

Total 12.6 378 677.2 29.5 29644

?̂=143.55−38.36? ???=1357.77

Using above information:

a. The price of candy in a city is $3.50. What is the sale estimate for the city?

b. Compute the standard error of the estimate.

c. Compute the coefficient of determination r² and interpret it meaning in this problem.

d. At a significance level of .01 can you conclude that the Price is a good predictor of the Sales.

Answer 1

a. The price of candy in a city is $3.50. What is the sale estimate for the city?

y = 143.55−38.36*3.50

y = 9.29

b. Compute the standard error of the estimate.

The standard error of the estimate is 18.424.

c. Compute the coefficient of determination r² and interpret it meaning in this problem.

r² = 0.767

76.7% of the variation in the model is explained.

d. At a significance level of .01 can you conclude that the Price is a good predictor of the Sales.

The hypothesis being tested is:

H0: β1 = 0

H1: β1 ≠ 0

The p-value is 0.0222.

Since the p-value (0.0222) is greater than the significance level (0.01), we fail to reject the null hypothesis.

Therefore, we cannot conclude that the Price is a good predictor of the Sales.