help with 2.5- 2.6 and 2.8

QUESTION 2 The gala dataset, found in faraway package, is a dataset on the species diversity on the Galapagos Islands. The data were collected to study the relationship between the number of plant species and various geographic variables. The dataset contains 30 Galapagos islands and seven variables. 2.1 Use the R code summary () to produce the summaries of the gala dataset. Please include the statistical output. (4) 2 2.2 Produce a scatter plot matrix and the correlation matrix of the predictors to investigate the correlation between the predictors. Based on your investigation, which covariates seem to be most strongly involved in multicollinearity? Elaborate. (10) 2.3 Using variance inflation factors, can you say that there is evidence of collinearity? Explain.(6) 2.4 Give the fitted multiple linear regression model and interpret the regression coefficients. (Note: do not include the variable "endemic" in the model). (8) 2.5 Discuss the significance of each regression coefficient in the fitted multiple linear regression model. Use a 5% level of significance. For each test provide the null and alternative hypothe- ses, critical region (or rejection region), test statistics and your conclusions. (18) 2.6 Plot the 95% confidence region for the parameters associated with "Elevation and Nearest". The location of the origin on the plot tells us the outcome of a certain hypothesis test. State the test and discuss the result. (6) 2.7 Use residual plots to answer the questions that follow: (a) Is the assumption of constant error variance violated? Give reasons for your answer. (3) (b) Is the assumption of normality of error terms violated? Give reasons for your answer.(3) (C) Would it be reasonable to leave the response variable untransformed? Give reasons for your answer. (2) 2.8 Use AIC to select the "best" model. (5) [65] QUESTION 2 The gala dataset, found in faraway package, is a dataset on the species diversity on the Galapagos Islands. The data were collected to study the relationship between the number of plant species and various geographic variables. The dataset contains 30 Galapagos islands and seven variables. 2.1 Use the R code summary () to produce the summaries of the gala dataset. Please include the statistical output. (4) 2 2.2 Produce a scatter plot matrix and the correlation matrix of the predictors to investigate the correlation between the predictors. Based on your investigation, which covariates seem to be most strongly involved in multicollinearity? Elaborate. (10) 2.3 Using variance inflation factors, can you say that there is evidence of collinearity? Explain.(6) 2.4 Give the fitted multiple linear regression model and interpret the regression coefficients. (Note: do not include the variable "endemic" in the model). (8) 2.5 Discuss the significance of each regression coefficient in the fitted multiple linear regression model. Use a 5% level of significance. For each test provide the null and alternative hypothe- ses, critical region (or rejection region), test statistics and your conclusions. (18) 2.6 Plot the 95% confidence region for the parameters associated with "Elevation and Nearest". The location of the origin on the plot tells us the outcome of a certain hypothesis test. State the test and discuss the result. (6) 2.7 Use residual plots to answer the questions that follow: (a) Is the assumption of constant error variance violated? Give reasons for your answer. (3) (b) Is the assumption of normality of error terms violated? Give reasons for your answer.(3) (C) Would it be reasonable to leave the response variable untransformed? Give reasons for your answer. (2) 2.8 Use AIC to select the "best" model. (5) [65]