Assignment 11 Solutions - CE 93 Prof. Joan Walker, Spring...

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Unformatted text preview: CE 93 Prof. Joan Walker, Spring 2011 Assignment 11 Solutions Due 04/27/2011 11:10 AM 1. X is a normal random variable. X~N( ). Thus: Since all Xi’s are normally distributed independent random variables with mean it turns out is also normally distributed, with mean and variance . and variance , Following the above, has a normal distribution with mean and variance . Again, we standard by subtracting its mean and dividing it by its variance, yielding 2. a) vs. Since b) , 5% significance we do not reject vs. Since c) , 10% significance we reject vs. Since at the 5% level. at the 10% level. , 5% significance we reject at the 5% level. d) Test the equality of variances at =0.8391, Since Therefore, the above assumption is reasonable. significance level. , we do not reject the hypothesis of equal variances. CE 93 3. Prof. Joan Walker, Spring 2011 a) Scatterplot 26 24 22 20 18 16 14 12 10 8 6 5 10 15 20 b) Linear curve fit 30 25 y 20 15 10 5 5 10 15 x Matlab code : scatter(x,y) hold on, plot(x,y1), hold off xlabel('x'),ylabel('y') 20 CE 93 4. a) Prof. Joan Walker, Spring 2011 3200 3000 2800 2600 2400 2200 2000 1800 1600 0.39 0.4 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 b) c) Since , is an unbiased estimator of . SSR=8.4528e+005 d) H0: H1: =0 0 TS= =2.74 t0.005,8=3.355; t0.025,8=2.306; t0.05,8=1.860 t0.05,8< t0.025,8<TS< t0.005,8 Therefore we don’t reject H0 at 1% significance level, but reject H0 at 5% and 10% significance levels. e) x=0.43, y=2439.8 CE 93 5. a) Prof. Joan Walker, Spring 2011 4000 3500 3000 2500 2000 1500 1000 500 0 0 500 1000 1500 2000 2500 3000 3500 4000 b) c) Test versus reject d) E(Y|X=2500)=2459.7 e) 95% prediction interval 5% level of significance. CE 93 Prof. Joan Walker, Spring 2011 [ : f) 2 1.5 1 0.5 0 -0.5 -1 0 500 1000 1500 2000 2500 3000 3500 4000 g) The standard residuals look random, and 95% (in this case of n=10, all observations) are between -2 and 2. ...
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This note was uploaded on 06/02/2011 for the course CIV ENG 93 taught by Professor Staff during the Spring '08 term at University of California, Berkeley.

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