**Unformatted text preview: **>summary(lm(y˜x)) Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.66 0.16 4.00 0.016 x 0.12 0.003 41.24 2.07e-06 Multiple R-Squared: 0.9977 Example 2. Suppose that data ( x j , y j ) satisfy a circular rela-tionship Y j = q 10 2-x 2 j + ± j . This is a nonlinear relation-ship so we expect not to have a good linear fit. 30 40 50 60 70 80 5 6 7 8 9 10 x y Figure 1: Hooke’s law.-10-5 5 10 2 4 x Figure 2: Complete lack of linear fit. >x<--10:10 >y<-sqrt(10ˆ2 -xˆ2) >summary(lm(y˜x)) Coefficients: value Pr(>|t|) (Intercept) . ... 1.24e-09 x .... 4.47e-17 Multiple R-Squared: 1.378e-030 Self-study problems Construct 100(1-α )% confidence intervals for both β and β 1 . Show Var ( ˆ β ) = σ 2 x 2 /S xx . Example 12.9....

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- Fall '04
- Chung
- Statistics, Coefficient Of Determination, Normal Distribution, Regression Analysis, Variance, Pearson product-moment correlation coefficient, SST