ch2exercisesol - STA 302 1001(A Gibbs Sketch of Solutions...

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Unformatted text preview: STA 302 / 1001 (A. Gibbs) Sketch of Solutions to Exercises in Chapter 2 of Sheather 1. (a) t 16 , . 025 = 2 . 12 95% CI for β 1 : 0 . 982 ± 2 . 12(0 . 014) = (0 . 95 , 1 . 01) Since 1 is in the CI, it is a plausible value for β 1 . (b) Test statistic: (6805- 10000) / 9929 =- . 32 From a t-distribution with 16 degrees of freedom, the p-value is 0.75 (from tables, can estimate that p > . 5) so the data give no evidence against the null hypothesis and we cannot rule out that the intercept is 10000. (c) ˆ y = 6805 + 0 . 982 * 400000 = 399605 95% PI: 399605 ± 2 . 12 * 18008 q 1 + 1 18 + (400000- 622187) 2 17 * 91642100481 = (359800 , 439400) Since $450,000 is not in the prediction interval, it is not a feasible value. (d) The proposed prediction rule is a reasonable estimate for shows with box office results near $378000 (where the regression line crosses the line y = x ). But these data illustrate the phenomenon of regression to the mean: shows with low box office results in the previous week on average have higher box office results...
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ch2exercisesol - STA 302 1001(A Gibbs Sketch of Solutions...

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