USE R CODE ! l. (15points) Let E(XIX,X,]= +AX, +Bx, ry | X) = 3, corr(X, , x 2 )
ID: 3062128 • Letter: U
Question
USE R CODE !
l. (15points) Let E(XIX,X,]= +AX, +Bx, ry | X) = 3, corr(X, , x 2 )-0, use ° = 1, , = 2.5 and Po =-4.5 where X is from an exponential distribution with -2 and X2 is from a normal distribution and p)- with mean and variance equal to 5 and 4, respectively. Generate data of size n-100 from the above linear regression model Find the estimated values of the coefficients and compare your results to the actual values of the parameters (ie. Repeat the simulation m=1000 times. At each of 1000 simulations, you used to generate a sample (X, i-I,.. ., À andß for each sample. Put the 1000 results in vectors (of length 1000) and named beta0, betal and beta2. Based on these vectors construct 95% confidence intervals for their corresponding parameters a) b) = 1, B = 2.5 and 2 =-4.5). c) 100) and compute Po, 9 B ). Do all your confidence intervals capture the true parameters? , B and ExplainExplanation / Answer
a)> x1=rexp(100,2)
> x1
[1] 0.025556132 0.022346383 0.212924642 0.496049710 2.413000176 0.601597859
[7] 0.264753695 0.119927783 1.419814755 0.197278909 0.110577109 0.303278627
[13] 0.073558394 0.298720550 1.801421250 0.352111282 0.172355233 1.617273599
[19] 0.060922395 0.005636613 0.032269982 0.256356373 0.132786680 0.009934823
[25] 0.437776804 0.384064039 0.061777105 0.335371396 1.428199951 0.557289436
[31] 1.256390576 0.234969792 0.162203522 0.015146382 0.023045689 0.064978909
[37] 0.043052675 0.442712621 0.280580676 1.193189482 0.202585069 0.314621245
[43] 0.591562662 0.704716473 0.378779832 0.094330906 0.745851056 0.931526856
[49] 0.989600046 0.241002552 0.073433295 0.248047422 1.613077009 0.684872819
[55] 0.462604267 0.285260143 0.269957577 0.639238060 0.605188325 0.437005434
[61] 0.205930484 0.294837863 0.526538600 0.173187936 0.002134417 0.162259401
[67] 0.612937768 0.459184221 0.351866279 0.007725520 0.448984679 0.105846166
[73] 0.176321571 1.270682498 0.090829289 0.484636614 0.313453590 0.924853341
[79] 0.312794790 0.422067608 0.094386056 0.192034708 0.040929495 0.773310581
[85] 1.169998811 0.075403901 0.103573287 0.146835771 0.085720731 0.176127765
[91] 0.102256077 1.324445787 2.149743717 0.156336491 0.338822813 0.048879769
[97] 0.978666378 0.621914018 1.483770523 0.272039614
> x2=rnorm(100,mean=5,sd=2)
> x2
[1] 4.412672 5.975349 6.147232 7.535683 3.075406 1.744157 4.874315 5.693750
[9] 8.747638 4.705843 5.036822 8.057918 6.746275 3.038167 3.632952 3.977254
[17] 4.549229 4.108453 3.239251 3.042585 6.607106 6.656722 6.645295 4.804051
[25] 6.620488 5.292727 4.749650 3.598026 7.863563 6.884531 3.829805 3.178774
[33] 4.142992 3.493848 4.360491 4.310189 4.601133 6.318987 3.484790 4.081611
[41] 5.602544 3.629180 5.320744 4.812083 3.851385 3.207539 4.990185 1.391171
[49] 7.758289 4.208086 3.338426 1.990169 6.854620 4.811177 4.971954 6.018483
[57] 4.976927 3.111290 3.204968 4.629448 2.739393 6.639904 4.040123 1.573684
[65] 4.783076 7.828186 4.287972 2.837380 2.123665 3.099300 5.020097 5.140899
[73] 1.019696 5.327693 8.859025 4.757856 4.720220 5.416341 5.560323 4.719747
[81] 4.286452 2.319494 3.269841 6.817321 6.970857 6.104847 2.590532 5.119868
[89] 9.662963 5.457493 5.860101 4.652739 4.156882 7.857977 7.291610 4.648284
[97] 6.668597 7.489231 3.564084 3.334666
> y=1+2.5*x1-4.5*x2
> y
[1] -18.793132 -25.833205 -26.130234 -31.670451 -6.806828 -5.344710
[7] -20.272534 -24.322054 -34.814832 -19.683095 -21.389255 -34.502435
[13] -29.174341 -11.924951 -10.844732 -16.017364 -19.040643 -13.444855
[19] -13.424323 -12.677543 -28.651304 -28.314356 -28.571862 -20.593391
[25] -27.697753 -21.857110 -20.218984 -14.352688 -30.815534 -28.587167
[31] -13.093145 -12.717058 -17.237956 -14.684451 -18.564594 -18.233404
[37] -19.597467 -26.328662 -13.980102 -14.384276 -23.704987 -14.544756
[43] -21.464444 -18.892582 -15.384284 -13.198099 -19.591206 -2.931452
[49] -31.438300 -17.333882 -13.839335 -7.335642 -25.813097 -18.938114
[55] -20.217282 -25.370023 -20.721278 -11.402708 -11.909384 -18.740001
[61] -10.812441 -28.142473 -15.864205 -5.648609 -20.518507 -33.821190
[67] -16.763529 -10.620249 -7.676829 -12.927535 -20.467975 -21.869431
[73] -3.147829 -19.797911 -38.638537 -19.198759 -19.457358 -21.061401
[79] -23.239467 -19.183691 -18.053069 -8.957637 -13.611962 -27.744670
[85] -27.443860 -26.283303 -10.398459 -21.672315 -42.269031 -23.118398
[91] -25.114812 -16.626211 -12.331609 -33.970054 -30.965189 -19.795079
[97] -26.562020 -31.146755 -11.328951 -13.325898
b)> model=lm(y~x1+x2)
> summary(model)
Call:
lm(formula = y ~ x1 + x2)
Residuals:
Min 1Q Median 3Q Max
-5.358e-15 -8.291e-16 5.620e-17 9.104e-16 5.755e-15
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.000e+00 4.771e-16 2.096e+15 <2e-16 ***
x1 2.500e+00 3.135e-16 7.975e+15 <2e-16 ***
x2 -4.500e+00 8.895e-17 -5.059e+16 <2e-16 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.555e-15 on 97 degrees of freedom
Multiple R-squared: 1, Adjusted R-squared: 1
F-statistic: 1.297e+33 on 2 and 97 DF, p-value: < 2.2e-16
Warning message:
In summary.lm(model) : essentially perfect fit: summary may be unreliable
c)> beta0=0
> beta1=0
> beta2=0
> for(i in 1:1000)
+ {
+ x1=rexp(100,1/2)
+ x2=rnorm(100,5,2)
+ y=1+2.5*x1-4.5*x2
+ model=lm(y~x1+x2)
+ beta0[i]=coefficients(model)[1]
+ beta1[i]=coefficients(model)[2]
+ beta2[i]=coefficients(model)[3]
+ }
> beta0
[1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[38] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[112] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[149] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[186] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[223] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[260] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[297] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[334] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[371] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[408] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[445] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[482] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[519] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[556] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[593] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[630] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[667] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[704] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[741] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[778] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[815] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[852] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[889] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[926] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[963] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[1000] 1
> beta1
[1] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[19] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[37] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[55] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[73] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[91] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[109] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[127] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[145] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[163] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[181] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[199] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[217] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[235] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[253] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[271] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[289] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[307] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[325] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[343] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[361] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[379] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[397] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[415] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[433] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[451] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[469] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[487] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[505] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[523] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[541] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[559] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[577] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[595] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[613] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[631] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[649] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[667] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[685] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[703] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[721] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[739] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[757] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[775] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[793] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[811] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[829] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[847] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[865] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[883] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[901] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[919] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[937] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[955] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[973] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
[991] 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5
> beta2
[1] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[15] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[29] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[43] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[57] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[71] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[85] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[99] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[113] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[127] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[141] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[155] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[169] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[183] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[197] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[211] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[225] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
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[463] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[477] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
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[533] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
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[561] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
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[589] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[603] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[617] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[631] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[645] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[659] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[673] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[687] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[701] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[715] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[729] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[743] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[757] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[771] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[785] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[799] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[813] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[827] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[841] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[855] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[869] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[883] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[897] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[911] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[925] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[939] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[953] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[967] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[981] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
[995] -4.5 -4.5 -4.5 -4.5 -4.5 -4.5
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