2 a) Write an R function which takes two vectors of data and performs the pooled two- sample Student's t test of of equality of means returning the test statistic and p-value as well as a statement of the conclusion at a specified level of significance defaulting to 0.05. Use your function to test for equality of the means of the following two samples r 6.35 3.47 6.54 6.21 8.72 10.43 y| 8.99 10.94 9.88 11.50 9.90 11.89 12.10 9.33 b) Forward selection is a model-selection process in linear regression in which we wish to model the response variable Y as a linear function of a subset of potential covariates 1,.. ., Xp. The method first checks all single covariate models and selects the one for which the covariate has the smallest p-value provided it is less than some pre-specified level. It then tries to add selecting the model with the most significant added variable. The process continues trying to add one covariate at a time and terminates when a model is found such that none of the remaining covariates have a sufficiently small p-value when added to the model Using a loop and the lm function, construct your own function that takes a response variable and a data.frame of potential covariates and applies forward selection. Your function should return some information ab as the final model Apply your function to the nuclear dataset which you can get as part of the boot package. a second variable to the selected one variable model, again out the order of adding the variables as well 2 a) Write an R function which takes two vectors of data and performs the pooled two- sample Student's t test of of equality of means returning the test statistic and p-value as well as a statement of the conclusion at a specified level of significance defaulting to 0.05. Use your function to test for equality of the means of the following two samples r 6.35 3.47 6.54 6.21 8.72 10.43 y| 8.99 10.94 9.88 11.50 9.90 11.89 12.10 9.33 b) Forward selection is a model-selection process in linear regression in which we wish to model the response variable Y as a linear function of a subset of potential covariates 1,.. ., Xp. The method first checks all single covariate models and selects the one for which the covariate has the smallest p-value provided it is less than some pre-specified level. It then tries to add selecting the model with the most significant added variable. The process continues trying to add one covariate at a time and terminates when a model is found such that none of the remaining covariates have a sufficiently small p-value when added to the model Using a loop and the lm function, construct your own function that takes a response variable and a data.frame of potential covariates and applies forward selection. Your function should return some information ab as the final model Apply your function to the nuclear dataset which you can get as part of the boot package. a second variable to the selected one variable model, again out the order of adding the variables as well