please solve this.

In this question you will be working with dataset longley which can be view in R by running the code data(longley). The objective is to predict the number of people employed from economic variables. You'll need to conduct most of your anal- ysis in R and produce screenshot of the output together with suitable comments. The dataset has several numerical columns: GNP.deflator, GNP, Unemployed, Armed. Forces, Population, Year, Employed. The response variable is Em- ployed. (i) Write down the formula for correlation coefficient for two random variables X and Y and use R to find pairwise correlation between the variables of longley. (5 marks) (ii) Create a multiple regression model regression Employed on all available vari- ables of the dataset. Produce a summary and ANOVA of the regression and comment on the significance of the parameter estimates. (5 marks) MATH1180 COURSEWORK 2 5 (iii) Hence using above produce a reduced model by selecting the most relevant ex- planatory variables and write the equation relating Employed to the relevant explanatory variables. (5 marks) (iv) State the assumptions underlying linear regression models. Produce the diag- nostic plots for your reduced model found in (iii) and comment on the validity of the model. (5 marks) (v) Produce a time series plot of Employed against years and produce the auto- correlation plot or values