The following output resulted from fitting a linear model using the log of Xt and the log of Yt, where Xt = index is a European (DAX) stock index and Yt = spread is the spread between EONIA and the central bank (ECB) deposit rate: Call: 1m (formula = log . spread ~ lag(log. index, -1) + lag(log. spread, -1) ) Residuals : Min 1Q Median 3Q Max -0. 50335 -0. 04691 -0. 00584 0. 04054 0. 46550 Coefficients : Estimate Std. Error t value Pr(>|t|) (Intercept) 0. 38539 0.52195 0. 738 0. 46066 lag (log. index, -1) -0. 06021 0. 05700 -1. 056 0. 29137 lag (log . spread, -1) -0. 06079 0. 02028 -2.998 0. 00286 ** Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1 Residual standard error: 0. 09241 on 479 degrees of freedom Multiple R-squared: 0. 01902, Adjusted R-squared: 0. 01493 F-statistic: 4.645 on 2 and 479 DF, p-value: 0. 01005 a. What are the explanatory variables of this model? [20%] b. Write the equation of the linear model based on this output. [20%] c. Consider the null hypothesis Ho: coefficient of first explanatory variable is zero versus HA: coefficient of first explanatory variable is non-zero. What quantity in the above output can be used for this test, and what is the result of the test at 90% confidence level? How does that change the model? Is the model an ARMA model? Justify your answer. [30%] d. Is there a statistically significant linear dependence between log Yt and log Yt-1 at the significance level 90%? [30%]