Stat 501 Sept. 15 Lab Activities Due no later than Friday Sept. 17Name _______________________________ e-mail UserID ___________________At the website www.stat.psu.edu/~rho/501data/) there is a link to a dataset named oldfaithful.mtw. Clickthe link, and Minitab will open with the data in place.The data are for n = 222 eruptions of the Old Faithful geyser in Yellowstone Park. The geyser erupts every 70 30 minutes. Variables are Duration = minutes an eruption lasts and TimeToNext = minutes until the next eruption. We’ll predict y = TimeToNext using x = Duration. That is, given the duration of a geyser eruption, how long will it be until the next eruption?1. Plot TimeToNext versus Duration. (Use Graph>Scatter Plot). Does the pattern appear to be linear? Do there appear to be any outliers? 2. Use Stat>Regression>Regression to find the regression equation for predicting TimeToNext (the response) using Duration (the predictor). What is the sample slope? Write a sentence that interprets this slope.3. Suppose that after an eruption of Duration = 2, the actual time until the next eruption is 56 minutes. What would be the value of the prediction error (also called residual) for this observation?4. In the output, what is the evidence that the observed relationship is “statistically significant?” Write the null hypothesis that is being tested, give the value of the t-statistic, and give the value of the p-value. 5. Determine a 95% confidence interval for the population slope. In Minitab, use Calc>Probability Distributions>t to find the necessary t-multiplier. (In the dialog box, click on Inverse Cumulative, enter df, and enter .975 as the Input Constant.6. Refer to the previous part. Write a sentence that interprets the confidence interval.7. Determine the multiplier that would be used for a 90% confidence interval for the population slope.8. In Minitab, return to Stat>Regression>Regression, use the Options button. In the box labeled “Prediction intervals for new values,” enter 4. This will cause Minitab to create information about predictions at x = 4. (That is, predicted time until next eruption when the present eruption is 4 minutes long.). Click OK enough times to get the output. What is the predicted (single) value of TimeToNext for Duration = 4? (it will be labeled Fit on the output) 9. Write the interval that describes the time until the next eruption for about 95% of the situations in which the present eruption is 4 minutes long. 10. The output includes the (approximate) information “S = 6.16.” Verify that the interval given in the previous part is roughly Predicted value 2 S. (Note: This won’t be exact so you’ll be off by 0.2 or so.) 11. Write the interval that estimates the mean time to the next eruption for all situations in which the present duration is 4 minutes.12. The output for the previous four parts gives the value of the standard error of yˆ(under SE Fit). Verifythat the confidence interval given in the previous part is roughly Predicted value (2 SE Fit). As in part 10, this isn’t the precise calculation so you’ll be off slightly.13. Determine the interval that predicts the time until next duration for 95% of the situations in which the present eruption lasts 2.5 minutes. 14. In Stat>Regression>Regression, use the Graphs button to create a graph of residuals versus fits for the regression that we’ve used for the previous parts. Explain whether the graph is evidence that the usual assumptions for a regression model are
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