13.1: Fitting a straight line to a set of data yields the following prediction line:
yt = 2 + 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 = 3.
13.2: If the values of X in Problem 13.1 range from 2 to 25, should you use this model to predict the mean value of Y when X equals
a. 3? b. -3? c. 0? d. 24?
Analytical Questions:
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 bagwithout 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. Datawere collected on 19 bags in which the gap plate 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 tear rating when the plate gap is equal to 0.
13.19: In problem 13.7, you used the plate gap on the bag-sealing equipment to predict the tear rating of a bag of coffee (stored in Starbucks). 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?
13.27: In problem 13.7, you used the plate gap on the bag-sealing equipment to predict the tear rating of a bag of coffee (stored in Starbucks). Perform a residual analysis for these data. Based on these results, evaluate whether the assumptions of regression have been seriously violated.
|
Tear
|
Viscosity
|
Pressure
|
Plate Gap
|
|
0.00
|
350.00
|
180.00
|
0.00
|
|
0.00
|
350.00
|
170.00
|
0.00
|
|
0.45
|
319.00
|
186.00
|
1.80
|
|
0.85
|
380.00
|
174.00
|
1.80
|
|
0.35
|
350.00
|
180.00
|
0.00
|
|
0.30
|
300.00
|
180.00
|
0.00
|
|
0.70
|
400.00
|
180.00
|
0.00
|
|
1.90
|
350.00
|
190.00
|
0.00
|
|
0.25
|
350.00
|
180.00
|
0.00
|
|
0.10
|
319.00
|
186.00
|
-1.80
|
|
0.15
|
380.00
|
186.00
|
-1.80
|
|
3.90
|
350.00
|
180.00
|
3.00
|
|
0.00
|
380.00
|
174.00
|
-1.80
|
|
0.55
|
350.00
|
180.00
|
0.00
|
|
0.00
|
350.00
|
180.00
|
-3.00
|
|
0.05
|
319.00
|
174.00
|
-1.80
|
|
0.40
|
319.00
|
174.00
|
1.80
|
|
4.30
|
380.00
|
186.00
|
1.80
|
|
0.00
|
350.00
|
180.00
|
0.00
|