In problem 13.7, you used the plate gap on the bag-sealing equipment to predict the tear rating
Question:
In problem 13.7, you used the plate gap on the bag-sealing equipment to predict the tear rating of a bag of coffee. Using the results of that problem,
a) Determine the coefficient of determination, R2, and interpret its meaning
b) Determine the standard error of the estimate.
c) How useful do you think this regression model is for predicting the tear rating based on the plate gap in the bag-sealing equipment?
(13.19)
Starbucks data:
| Tear | PlateGap |
| 0.00 | 0.00 |
| 0.00 | 0.00 |
| 0.45 | 1.80 |
| 0.85 | 1.80 |
| 0.35 | 0.00 |
| 0.30 | 0.00 |
| 0.70 | 0.00 |
| 1.90 | 0.00 |
| 0.25 | 0.00 |
| 0.10 | -1.80 |
| 0.15 | -1.80 |
| 3.90 | 3.00 |
| 0.00 | -1.80 |
| 0.55 | 0.00 |
| 0.00 | -3.00 |
| 0.05 | -1.80 |
| 0.40 | 1.80 |
| 4.30 | 1.80 |
| 0.00 | 0.00 |
Problem 13.7 already solved as reference:
13.7: 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. 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 gap plate was varied. The results are stored in Starbucks.
a) Construct a scatter plot
Here, X: Plate Gap and Y: Tear
b) Assuming a linear relationship, use the least-squares method to determine the SRF coefficient estimates ?0 and ?1.
Sum of X = 0Sum of Y = 14.25Mean X = 0Mean Y = 0.75Sum of squares (SSX) = 43.92Sum of products (SP) = 21.96Regression Equation = ? = bX + ab = SP/SSX = 21.96/43.92 = 0.5a = MY - bMX = 0.75 - (0.5*0) = 0.75Regression Line: ? = 0.5X + 0.75
c) Interpret the meaning of the slope, ?1, in this problem.
For every 1 unit increase in the plate gap on the bag-sealing equipment, the tear rating is expected to increase by 0.5 on an average.
d) Predict the tear rating when the plate gap is equal to 0.
For X = 0 , y = intercept = 0.75
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