A coffee company uses a data-based approach to improving the quality and custome

Question

A coffee company uses a data-based approach to improving the quality and customer satisfaction of its products. When survey data indicated that the coffee company 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. 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. Complete parts (a) through (e) below. Click the icon to view the data table. b. Assuming a linear relationship, use the least-squares method to find the regression coefficients b_0 and b_1. b_0 = 1 b_1 = (Round to four decimal places as needed.) c. Interpret the meaning of the slope. b_1, in this problem. Choose the correct answer below. A. For each one-unit increase in the plate gap, the tear rating is expected to increase by b_1. B. For each increase of one in the tear rating, the plate gap is expected to increase by b_1 units. C. The approximate tear rating when the plate gap is 0 units is b_1. D. The approximate plate gap when the tear rating is 0 is b_1 units. Click to select your answer(s).

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Tear Rating
Independent Variable: Plate Gap
Tear Rating = 0.68041386 - 0.31138486 Plate Gap
Sample size: 19
R (correlation coefficient) = -0.15765888
R-sq = 0.024856323
Estimate of error standard deviation: 1.2806605

Parameter estimates:

Analysis of variance table for regression model:

Hence,

bo = 0.6804

b1 = -0.3114

Meaning of slope: Option A

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.68041386 0.32279172 0 17 2.1079037 0.0502 Slope -0.31138486 0.47303024 0 17 -0.65827687 0.5192

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