Introduction to Probability and Statistics for Engineers and Scientists
364 Chapter 9: Regression Hypothesis Test ofH 0 :β=0 A significance levelγtest ofH 0 is to reject H 0 if √ (n−2)Sxx SSR |B|>t ...
9.4Statistical Inferences About the Regression Parameters 365 To compute the value of the test statistic, we first compute the v ...
366 Chapter 9: Regression REMARK The result that B−β √ σ^2 /Sxx ∼N(0, 1) cannot be immediately applied to make inferences aboutβ ...
9.4Statistical Inferences About the Regression Parameters 367 Father’s Height 75 70 65 60 55 Son’s Height 55 60 65 70 75 FIGURE ...
368 Chapter 9: Regression It now follows from Equation 9.4.2 that whenβ=1, the test statistic TS= √ 8 Sxx/SSR(B−1) has at-distri ...
9.4Statistical Inferences About the Regression Parameters 369 one-half of its parents’ genes, it follows that the offspring of, ...
370 Chapter 9: Regression 80 90 100 110 120 130 Deaths in 1988 120 110 100 90 80 Deaths in 1989 FIGURE 9.8 Scatter diagram of 19 ...
9.4Statistical Inferences About the Regression Parameters 371 Confidence Interval Estimator ofα The 100(1−a) percent confidence ...
372 Chapter 9: Regression variables and is thus itself normally distributed. Because we already know its mean, we need only comp ...
9.4Statistical Inferences About the Regression Parameters 373 EXAMPLE 9.4e Using the data of Example 9.4c, determine a 95 percen ...
374 Chapter 9: Regression the future response whose input level isx 0 and consider the probability distribution of the response ...
9.4Statistical Inferences About the Regression Parameters 375 Prediction Interval for a Response at the Input Levelx 0 Based on ...
376 Chapter 9: Regression Inferences About Use the Distributional Result α+βx 0 A+Bx 0 −α−βx 0 √√ √√ ( 1 n+ (x 0 −x)^2 Sxx )( SS ...
9.5The Coefficient of Determination and the Sample Correlation Coefficient 377 represents the amount of variation in the respons ...
378 Chapter 9: Regression near+1 indicated that largexvalues were strongly associated with largeY values and smallxvalues were s ...
9.6Analysis of Residuals: Assessing the Model 379 is appropriate in a given situation is to investigate the scatter diagram. Ind ...
380 Chapter 9: Regression 400 300 200 100 0 Random data and regression line x (^05101520) y 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 R ...
9.7Transforming to Linearity 381 9.7Transforming to Linearity In many situations, it is clear that the mean response is not a li ...
382 Chapter 9: Regression x P 0.6 0.5 0.4 0.3 0.2 0.1 0.0 020406080 FIGURE 9.10 Example 9.7a. SOLUTION LetP(x) be the percentage ...
9.7Transforming to Linearity 383 TABLE 9.2 Temperature −log(1−P) 5 ◦ .063 10 ◦ .120 20 ◦ .213 30 ◦ .300 40 ◦ .414 50 ◦ .512 60 ◦ ...
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