Predictive Modeling
预测建模代写 Return to the full dataset of n = 185 countries and run a regression model using FERTILITY, FUBLICEDUCATION, and lnHEALTH as explanatory variables.
Homework 5 预测建模代写
1.ANOVA one factor Data File Table 6.25-PlasmaPhosphate.xls Please refer to Dobson Exercise 6.5 and answer the following questions
(a) Test the hypothesis that there are no mean differences among the three groups.
(b) Assume independent groups and normality with common variance, obtain a 95% confidence interval for the difference in means between the hyperinsulinemic obese group and the nonhyperinsulinemic obese group.
(c) Using an appropriate model, plot the standardized residuals against the observation index. Also produce a normal probability plot for the standardized residuals.
2.ANOVA two factors with unbalanced data Data File Table 6.27-UnbalancedData.xls
Please refer to Dobson Exercise 6.8 and answer the following questions.
(a) Test the hypothesis (at 5%) that there are no interaction effects
(b) Test the hypothesis (at 5%) that there is no effect due to Factor A by comparing the models
E [Yjkl] = µ + αj + βk E [Yjkl] = µ + βk
(c) Test the hypothesis (at 5%) that there is no effect due to Factor A by comparing the models
E [Yjkl] = µ + αj E [Yjkl] = µ
(d) Compare your conclusions for (b) and (c) and explain the difference.
3.National LIfe Expentancies. Referred to Frees’ Exercise 5.3 and 5.4. 预测建模代写
(a) Begin the data set from n = 185 countries that have valid (nonmissing) life ex-pectancy (LIFEEXP). (Note that: Check the whether data valid for a variable x, sum(data,is.na(x))). Plot the LIFEEXP versus GDP (gross domestic product) and PRIVATEHEALTH (private expenditures on health). From these plots, de scribe why it is desirable to use logarithmic transforms, lnGDP and lnHEALTH, respectively. ALso plot LIFEEXP versus lnGDP and lnHEALTH to confirm your intuition.
(b) Return to the full dataset of n = 185 countries and run a regression model using FERTILITY, FUBLICEDUCATION, and lnHEALTH as explanatory variables.
b.(i) Provide plots of standardized residuals.
b.(ii) Identify all outliers (outlier defined as the standardized residual greater then 3 in absolute value), (hint: which.is.max(x)).
b.(iii) Provide plot of leverage.
b.(iv) Identify all high leverages (high leverage defined as hii > 3 × ¯h). 预测建模代写
b.(v) Identify a data point if any that is both outlier and high leverage. Then calcu-late the cook’s distance for the point in b(iv), determine the decomposition of the distance, the attribution from outlier and high leverage respectively.
(c) Variance Inflation Factors.
c.(i) Brief explain the idea of of collinearity and a variance inflation factor.
c.(ii) What constitutes a large variance inflation factor?
c.(iii) Calculate the VIF for lnHEALTH by obtaining R.
c.(iv) Calculate all three explanatory variables without rerun the regression using the relation of VIF to se(bj ) that explained in class.
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