Introduction to Linear Regression Analysis. Douglas C. Montgomery

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      where tanh u = (eue−u)/(eu + e−u).

      Example 2.9 The Delivery Time Data

      Consider the soft drink delivery time data introduced in Chapter 1. The 25 observations on delivery time y and delivery volume x are listed in Table 2.11. The scatter diagram shown in Figure 1.1 indicates a strong linear relationship between delivery time and delivery volume. The Minitab output for the simple linear regression model is in Table 2.12.

      The sample correlation coefficient between delivery time y and delivery volume x is

ueqn57-2

       TABLE 2.11 Data Example 2.9

Observation Delivery Time, y Number of Cases, x
1 16.68 7
2 11.50 3
3 12.03 3
4 14.88 4
5 13.75 6
6 18.11 7
7 8.00 2
8 17.83 7
9 79.24 30
10 21.50 5
11 40.33 16
12 21.00 10
13 13.50 4
14 19.75 6
15 24.00 9
16 29.00 10
17 15.35 6
18 19.00 7
19 9.50 3
20 35.10 17
21 17.90 10
22 52.32 26
23 18.75 9
24 19.83 8
25 10.75 4

       TABLE 2.12 MlNITAB Output for Soft Drink Delivery Time Data

Regression Analysis: Time versus Cases
The regression equation is
Time = 3.32 + 2.18 Cases
Predictor Coef SE Coef T P
Constant 3.321 1.371 2.42 0.024
Cases 2.1762 0.1240 17.55 0.000
S = 4.18140 R- Sq= 93.0% R- Sq(adj) = 92.7%
Analysis of Variance
Source DF SS MS F P
Regression 1 5382.4 5382.4 307.85 0.000
Residual Error

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