8. (We make some statistics to determine R and make the ANOVA table) Determine SS, SS and SSR. Upload SSR. 9. Determine R of the regression. 10. (From here, ANOVA analysis) Calculate MS and MSR. Upload MSR. 11. Determine the TV of the test on the regression, i.e., Ho: B2=0. H1: Bıx0. 12. Determine the CV of the test on the regression at the significance level of 5%. 13. Determine if we can reject Ho at the significance level of 5%, where Ho: B=0.H1:31+0. (1) We reject Ho. (2) We cannot reject Ho.
Show all formulas and calculations involved in the solutions. Without all calculations given here, the entire HW will not get a credit. Let us consider these four data points and the regression line from Excel. We consider this simple near model: Y= Bo+B2x1+E. (Problems 1-13) Ylvibration levels Data 1 2 3 4 Sum Mean X(water pressure) 20 23 28 32 103 25.75 Y(vibration level) 120 140 145 180 585 146.25 31 10
1. n = 4, z = ΣΗ 25.75, y = 146.25, n n S. = z? - nă? = 84.75, Syy = 12 - ný? = 1868.75, Sxy=xy - nwy = 376.25. Say - 2. Ŝi = estimate of the slope 4.439528 SET Bo = estimate of y-intercept = y - Byx = 31.932153. Sky 0.9454336. 3. r = sample correlation coefficient = SuzSyy ? (1 - 12) Syy 99.18879 n-2 4. se(i) = estimate of standard error of B = 1.081836 S. .22 se(Bo) = estimate of standard error of Bo = 1+ = 28.29885. S (30 - 2)2 5. sè(muy 1 == 3) = 2 = 6.777683. S, 6. Upper limit of 95% CI for B1 = B1 + 0.025, 2 (ßı) = 9,0943 n where, to.025,2 = 4.3027 (Use R code: round(qt(0.975, 2), 4)). 7. Upper bound= HY] =30 + to, 25,2 se (ay|x=30) = 194.28 where, fly|=30 = 165.118
8. (We make some statistics to determine R and make the ANOVA table) Determine SS, SS and SSR. Upload SSR. 9. Determine
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8. (We make some statistics to determine R and make the ANOVA table) Determine SS, SS and SSR. Upload SSR. 9. Determine
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