Forcasting review_midterm_II_Solutions

# Forcasting review_midterm_II_Solutions - STAT 373 F08...

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STAT 373 F08 Review Midterm II 1) The following partial data and plot is from a dataset on the number of users logged on to an Internet server each minute over 100 minutes. (Source: http://wwwpersonal.buseco.monash.edu.au). Suppose you wish to fit a ARMA model to forecast the number of internet users in the 101th minute. Minute Number of Internet Users M M 98 226 99 222 100 220 0 2 04 06 08 01 0 0 100 150 200 Minute Number of Users a) Output from a AR(1) fit to the differences, { } where t z z z ,..., , 3 2 1 = i i i y y z , i = 2,…100 is given below. Call: arima(x = intdiff, order = c(1, 0, 0)) Coefficients: ar1 intercept 0.7939 1.0209 s.e. 0.0597 1.6057 Predict the number of Internet users in the 101th minute of this process. 38 . 1 ) 0209 . 1 2 ( 7939 . 0209 . 1 ) ˆ ( ˆ ˆ ˆ 1 = + = + = + μφ μ t t z z 62 . 218 38 . 1 220 ˆ ˆ 1 1 1 = = + = + + + t t t z y y b) Based on this AR (1) output , is there evidence of a mean minute-to-minute increase in the number of users over this time period? μ ˆ μ is not significantly different from 0 (i.e., a 95% confidence interval μ

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STAT 373 F08 Review Midterm II 2) The following table contains data from the last six observations of the paint flowrate dataset from your course notes. Observed and predicted values (rounded for convenience) based on an EWMA smooth ( α = .30) for the last six values (from left to right) are presented below. Flowrate
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Forcasting review_midterm_II_Solutions - STAT 373 F08...

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