Is the model in part 2 adequate if not modify the model and

Question

The data set Fbylds.txt contains observations on the monthly Fama-Bliss bond yields with maturities 1 and 3 years obtained from CRSP. Let y_1t and y_3t denote the yields with maturities 1 and 3 years respectively.

qdate = date YYYYMMDD

yield1 = bond yield with 1 year maturity

yield3 = bond yield with 3 year maturity

Instructions:

(1) To upload the data set into R, use read. table 0.

(2) For your answers, hand in only the print of the script for your R commands along with your explanations.

Questions:

(1) Fit the linear regression model

Y_3t = β₀ + β₁γlt + e_t.

Write down the fitted model. What is the R²? Is the model adequate? Why?

(2) Let d_lt = (1 - B)y_lt and d_2t = (1 - B)y_3t, where B is the back-shift operator and d_it is the change in monthly bond yields. Consider the linear regression model

d_3t = β₀ + β₁d_lt + e_t

Write down the fitted model. What is the R²? Explain why it is appropriate to take the first difference of the bond yields.

(3) Is the model in part (2) adequate? If not, modify the model and write down the new model.

(4) Based on the modified model, describe the linear dependence between the bond yields.

(5) Suppose that you are concerned with taking the first difference. Fit the AR(6) model to y_3t using y_1t as an explanatory variable along with an intercept. Write down the down the fitted model.

(6) Modify the model by letting insignificant coefficients of lags 2 and 5 be zero. Write down the fitted model.

Is the modified model adequate? Why?

I am trying to get help with the home work attached. It is due tonight and I thought I could have done it in time but I can't. Need help ASAP.