代写ETC2560 ETC5256 Class Test 2024帮做R编程

日期：2024-10-17 06:48

ETC2560 ETC5256 Class Test 2024

Q1       The data below are obtained from a general insurance portfolio. Estimate Kendall’s tau between the two variables and perform. a statistical test on its significance. Show your work clearly.

Q2      Use the eigenvalues of covariance matrix method to perform. the principal component

analysis (PCA on the data  Show your steps clearly.

Q3       The following results are generated from applying a linear regression model with one explanatory variable to an insurance data set of 20 observations. Calculate the intercept and regression coefficient and test their statistical significance. Then deduce the 95% prediction interval of Y * when x * = 11.5. Show your work clearly.

   

Q4      A generalised linear model with the gamma distribution and the identity link function is applied to a large insurance data set. The computation results and the residual plots are shown below. Discuss whether the fitted model is suitable for the data set and suggest how it can possibly be improved, including how to modify the R code below.

> model<-glm(y~x1+x2,family=Gamma(link="identity"))

> summary(model)

Call:

glm(formula = y ~ x1 + x2, family = Gamma(link = "identity"))

Coefficients:

Estimate	Std. Error            t value	Pr(>|t|)
(Intercept)         0.97421	0.02220              43.883	<2e-16 ***

x1                         0.02559              0.03313              0.772                   0.44

x2                         2.01319               0.03580               56.234                 <2e-16 ***

Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘ .’ 0.1 ‘ ’ 1

(Dispersion parameter for Gamma family taken to be 0.0313481)

Null deviance: 125.904  on 999  degrees of freedom

Residual deviance:  33.107  on 997  degrees of freedom

AIC: 683.6