Questions and Answers of A Course In Statistics With R

Fit a simple linear regression model for the Galton dataset as seen in Example 4.5.1. Compare the values of the regression coefficients of the linear regression model for this dataset with the
Extend the concept of R2 and AdjR2 for the resistant line model. Create an R function which will extract these two measures for a fitter resistant line model and obtain these values for the
The Sign if. codes as obtained by summary (lm) may be easily customized in R to use your own cut-off points, and symbols too. There are two elements to this, first the cut-off points for the p-values
In Example 13.4.3, change the range of the variables x1 and x2 to x1 <- rep(seq(-10,10,0.5),100) and x2 <- rep(seq(-10,10, 0.5),each=100) and redo the three-dimensional plot, especially for the
For the fitted linear model crime_rate_lm, using the usc dataset, obtain the plot of residuals against the fitted values.
Verify the properties of the hat matrix H given in Equation 12.37 for the fitted object crime_rate_lm, or any other fitted multiple linear regression model of your choice.Data from in Equation
Identify which of the design models studied in this chapter are appropriate for the datasets available in the BHH2 package. The list of datasets available in the package may be found with
Multiple comparison tests of Dunnett, Tukey, Holm, and Bonferroni have been explored in Example 13.3.8. The confidence intervals are reported only for Tukey HSD. The reader should obtain the
Explore the use of the functions design.crd and design.rcbd from the agricolae package for setting up CRD and block designs.
The iris data has been introduced in AD2. Obtain the matrix of scatter plots for (i) the overall dataset (removing the Species), and (ii) three subsets according to the Species. Obtain the average of
For the board stiffness data discussed in Example 14.3.3, obtain the covariance matrix and then using the cov2cor function, obtain the correlation matrix.Data from in Example 14.3.3Four measures of
Run the example code of the function HotellingsT2, that is run example(HotellingsT2), and explore the options available with this function.
Carry out the MANOVA analysis for the iris datasets, where the hypothesis problem is that the mean of the multivariate vector of the four variables are equal across the three types of species.
Using base matrix tools of R, create a function which returns the value of Roy’s test statistic given in Equation 14.21.Data from in Equation 14.21 e= 서 1+₁ (14.21)
Repeat the above exercise for the Pillai and Lawley-Hotelling tests respectively given in Equations 14.22 and 14.23.Data from in Equations 14.22Data from in Equations 14.23 S λ; ΣΤΑ 1 +
Explore the R examples for linear discriminant analysis and canonical correlation with example (lda) and example (cancor).
Perform the PCA on the iris dataset along the two lines: (i) the entire dataset, (ii) three subsets according to the three species. Check whether the PC scores are significantly different across the
Obtain stacked bar plots for UCB Admissions, Hair Eye Color, and Titanic datasets.
From the Titanic dataset, obtain the odds ratio of survivors for the following: (i) Adult vs Child, (ii) Male vs Female, (iii) for each of the Class as in 1st, 2nd, 3rd, and Crew. For the UCB
Find the Wilson confidence interval for the probability of admission of a female candidate in the UCB Admissions data.

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