1.6.1: Illustration- The Missing Kraj

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Every 10 years of a king's reign, Ruritania holds a census. Their last was in 2020, marking King Rudolph's 80th year as monarch. After compiling all information, they discovered that information was missing for one kraj (state). This is unfortunate, because King Rudolph needs the information to evaluate his latest five-year plan and determine what he should do to make it better.

To fill in the missing information, we can regress all other variables on the GKP per capita, then predict the GKP per capita based on the known values for the missing kraj.

With this data and model, we just predict the GKP per capita in the kraj. The most-likely value is $2400, with a 95% prediction interval from $2100 to $2650.

From this information, His Majesty concludes that the plan helped the entire country, but did a better job with the rural areas than the urban. As a result of this analysis, he asks his ministers to generate a plan that does a better job of spreading the prosperity to more of the Kingdom.

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This use of regression has a very important use: Estimating values for missing data in a data set (imputation). Frequently, the amount of missing data will be significant with respect to the amount of complete data. In such a case, the researcher may use multiple imputation to create multiple data sets, estimate the parameters of interest on each, and report them and their standard errors.

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