We fit two models for simulated time series data Yt against Xt:(a) Write down the fitted linear regression. What is the R2 of the linear regression? Is the fitted model adequate? Why?(b) After reviewing the ACF and PACF plots. The researcher decided to fit the model 2 with time series errors for this simulated data. What is the fitted model? Write down the fitted model. What is the residual standard deviation of the model?(c) Based on the available output, is model 2 a good fit for the data? Why?m1<- lm(y~x, data=df2)summary(m1)Call:lm(formula = y ~x, data = df2)Residuals:Min 1Q Median 3Q Max-65.10 -18.51 -2.10 17.42 68.55Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 52.737 1.874 28.14 <2e-16 ***x 22.923 1.787 12.82 <2e-16 ***---Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1Residual standard error: 26.5 on 198 degrees of freedomMultiple R-squared: 0.4537, Adjusted R-squared: 0.451F-statistic: 164.5 on 1 and 198 DF, p-value: < 2.2e-16acf(m1$residual)pacf(m1$resi dual)Box. test(m1$residual, lag=10,type="Ljung")Box-Ljung testdata: m1$residualX-squared = 177.09, df = 10, p-value < 2.2e-16m2=arima(y, order = c(1,0,0), xreg = x)m2Call:arima(x = y, order = c(1, 0, 0), xreg = x)Coefficients:ar1 intercept x0.7084 52.6141 24.4899s. e. 0.0496 4.4589 1.0576sigma^2 estimated as 346.2: log likelihood = -868.84, aic = 1745.68Box. test(m2$residual, lag=10,type="Ljung")Box-Ljung testdata: m2$residualX-squared = 7.534, df = 10, p-value = 0.6743