Does not include 0 as a possible value for the slope

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does not include 0 as a possible value for the slope, it appears that the number of advance reservations is a useful predictor of the number of meals to be prepared in the context of a linear regression model, y = β 0 + β 1 x + ² . / £ ¡ ¢ EXAMPLE 11.2 Refer to the data of Example 11.1. Confirm the conclusion we receached concerning β 1 by conducting a test of H 0 : β 1 = 0 versus H a : β 1 6 = 0. Use α = . 10. Solution: The parts of the statistical test are given here: H 0 : β 1 = 0 H a : β 1 6 = 0 T.S. : t = ˆ β 1 s ² S XX = 0 . 67 17 . 44 90 , 000 = 11 . 53 R.R. : For a two-tailed test with α = . 10 and df = 98, we will reject H 0 if | t | > 1 . 645. Conclusion: Since t = 11 . 53 is greater than 1.645, we have sufficient evidence to reject H 0 . It does appear that x is useful in predicting y . 7
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8
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The Simple Linear Regression The dependent variable unknown model parameters β 0 : intercept; β 1 : slope independent variable Random error
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