Consider the following count models fitted using the glm command in R, between (i) Model 1: ycount(the response variable) and x1 (the covariate) and (ii) Model 2: ycount (the response variable) and x2 (the covariate). Model 1 Coefficients: Estimate Std. Error z value Pr (> |21) (Intercept) 0. 31014 0. 37034 0. 837 0 . 402 x1 -0. 13030 0 . 03219 -4.047 5. 18e-05 * * * Signif. codes: 0 ' * **' 0.001 '**' 0. 01 ' *' 0.05 . ' 0.1 \\ " 1 (Dispersion parameter for poisson family taken to be 1) Null deviance: 405.96 on 442 degrees of freedom Residual deviance: 389. 08 on 441 degrees of freedom AIC: 614. 79 Number of Fisher Scoring iterations: 6 Model 2 Coefficients : Estimate Std. Error z value Pr(> |z1) (Intercept) -1. 50472 0. 40640 -3. 703 0. 000213 * * * x2 [1 : 150] -0. 07451 0. 38090 -0. 196 0. 844917 Signif. codes: 0 ' * * *' 0. 001 '**' 0. 01 ' *' 0.05 .' 0.1 \\ ' 1 (Dispersion parameter for poisson family taken to be 1) Null deviance: 115.43 on 149 degrees of freedom Residual deviance: 115.40 on 148 degrees of freedom AIC: 172. 84 Number of Fisher Scoring iterations: 6 (a) Write down the two R-commands that produced the above output for model 1 and model 2 (this should be two lines of commands: one line for model 1 and another line for model 2). (b) In terms of goodness of fit, briefly explain how you would compare the two models using the above output. Between model 1 and model 2, which model would you say offers a better fit? Explain. (c) Write down the fitted regression model for model 1 and provide an interpretation for the slope coefficient (Coefficient of x1) (d) Compute the expected response counts for x1 = 2 and x1 = 10. How would you inter- pret your result for al = 10