Esami metodi statistici, Esercizi di Metodi Statistici Per L'impresa

Scarica Esami metodi statistici e più Esercizi in PDF di Metodi Statistici Per L'impresa solo su Docsity! Business Statistics (a.y. 2012-13) Name ................................. Surname .............................. Matricola ............... Signature....................... 1) Given A and Ac :  P(A∪Ac)=0    P(A∩Ac)=1    P(A∩Ac)=P(A)    P(A∪Ac)=P(A)+P(Ac)   2) Given A and B, where A is included in B (A⊂B) :  P(A∩B)=P(A)P(B)   P(A∩B)=P(A|B)P(B)   P(A∩B)=P(A)   P(A∩B)=P(B)  3) Given a Normal r.v. X, with E(X)= -1 and standard deviation σ=4, and a Standard Normal r.v. Z:  P ‐5 X 9 P ‐3 Z 4     P ‐5 X 9 P ‐1.5 Z 2  P ‐5 X 9 P ‐2 Z 5  P ‐5 X 9 P ‐1 Z 2.5 4) For a biased estimator T the MSE is:  MSE(T)=V T E T ‐θ 2  MSE(T)=E T‐θ 0   MSE(T)=V T  MSE(T)=E T‐E T 0 5) For a test statistic the p-value is 0.005:  we accept the null hypothesis for α-level=0.05  we reject the null hypothesis for α-level=0.01  we accept the null hypothesis for α-level=0.01  we reject the alternative hypothesis for α-level=0.01 6) Considering the output1, calculate the value of F-test (explain the result). F=1042600.9/122644.539=8.5 7) Considering the t-test in output1, are there regression coefficients significantly different from zero at an α-level=0.05?(explain the result) age , ne 8) Considering the output1, what is the value of the t test for ne? (explain the result) t=352.4107 / 103.138= 3.417 9) Considering the output2, if the years of education increase, the probability of losing the job after the sixth month:  decreases  rises  does not vary  decreases of 0.00757 10) Considering the output2, is it possible to accept the null hypothesis that all regression coefficients are null? (explain the result) No, because Prob>chi2=0.0000<α 11) If odds=0.5, the probability of success, Pr(Y=1|X), is:  0.66  0.33  1  -0.66 12) Which are the assumptions on the response variable in the logit model? Y∼Be(π) independent 13) In output2, what is the interpretation of the regression coefficient for sex? The odds for female is exp(0.476)=1.61 times the odds for male. So, the probability to lose the job after the sixth month for a female is higher than for a male. 14) In output3, calculate sensitivity, specificity and the correctly classified rate sensitivity=14.21% specificity=97.40% correctly classified rate=75.11% 15) Which of the following statements is true? Principal Components  are uncorrelated with each other  all have the same variance  uncorrelated with the observed variables  have mean equal to 1