3 Fitting a straight line to a set of data yields the following prediction line: Yn i = 16 - 0.5Xi a. Interpret the meaning of the Y intercept, b0....

12.3 Fitting a straight line to a set of data yields the following

prediction line:

Yn

i = 16 - 0.5Xi

a. Interpret the meaning of the Y intercept, b0.

b. Interpret the meaning of the slope, b1.

c. Predict the value of Y for X = 6.

Starbucks Coffee Co. uses a data-based approach to improving

the quality and customer satisfaction of its products.

When survey data indicated that Starbucks needed to improve its

package-sealing process, an experiment was conducted to determine

the factors in the bag-sealing equipment that might be affecting

the ease of opening the bag without tearing the inner liner

of the bag. (Data extracted from L. Johnson and S. Burrows, “For

Starbucks, It’s in the Bag,” Quality Progress, March 2011,

pp. 17–23.) One factor that could affect the rating of the ability of

the bag to resist tears was the plate gap on the bag-sealing equipment.

Data were collected on 19 bags in which the plate gap was

varied. The results are stored in Starbucks .

a. Construct a scatter plot.

b. Assuming a linear relationship, use the least-squares method to

determine the regression coefficients b0 and b1.

c. Interpret the meaning of the slope, b1, in this problem.

d. Predict the mean tear rating when the plate gap is equal to 0.

e. What should you tell management of Starbucks about the relationship

between the plate gap and the tear rating?