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I have most of this question done. I would like my work checked for problem 1 parts a - d i. I am stuck on d ii and e and need some help. I will upload my work once a tutor responds.

**1**. Use the Ã¢LakeErieÃ¢ dataset. One column of the dataset gives water levels of Lake Erie for *n* = 40 consecutive Novembers and another gives the lag 1 values of the series. The lag 1 value is the value from the previous year.

(a)Â Â Â Do a time series plot of the variable NovLevel. That is, plot the NovLevel in time order. [In Minitab, use Graph** > **Time Series Plot.] Is there any obvious upward or downward trend to the Lake Erie levels?

(b)Â Â Â Plot NovLevel against the lag 1 values. Describe the noteworthy features of the plot.

(c)Â Â Â Determine the partial autocorrelations for the NovLevel series. [In Minitab, use Stat**Â > **Time Series** > **Partial Autocorrelation, enter NovLevel as the variable (or series) and click OK.] What do the results indicate about the autoregression order for a model that describes November water levels of Lake Erie?

(d)Â Â Â Do a simple regression with NovLevel as the response and lag 1 values of NovLevel as the predictor variable. Use the Storage button to store the residuals. (Note: This is a first-order autoregression model for the series.)

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â i.Â Â Â Â Â Â Â Â Â Â Â Write the estimated regression equation.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ii.Â Â Â Â Â Â Â Â Â Â Â Use the regression equation to find the fitted value of the November water level of Lake Erie in the next year after the final year of the data series. [For this question you *donÃ¢t* need to use the method at the bottom of Section 14.3.]

(e)Â Â Â Determine partial autocorrelations for the residuals from the regression that you did in part (d). [In Minitab, use Stat** > **Time Series** > **Partial Autocorrelation, enter RESI1 as the variable (or series) and click OK.] What do the results indicate? (Note: The residuals ideally are a random sample, which means that they should have no time series structure to them. That is, ideally, any partial autocorrelations should have values near 0.)

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