Introduction to Linear Regression Analysis. Douglas C. Montgomery
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where tanh u = (eu − e−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
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
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The regression equation is
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Time = 3.32 + 2.18 Cases
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Predictor
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Coef
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SE Coef
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T
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P
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Constant
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3.321
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1.371
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2.42
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0.024
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Cases
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2.1762
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0.1240
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17.55
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0.000
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S = 4.18140
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R- Sq= 93.0%
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R- Sq(adj) = 92.7%
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Analysis of Variance
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Source
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DF
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SS
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MS
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F
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P
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Regression
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1
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5382.4
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5382.4
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307.85
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0.000
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Residual Error
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