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Statistical Methods in Business and Economics

Statistical Methods in Business and Economics

Question No. 1

For the following scatter plot, what would be your best estimate of the correlation coefficient?

Scatter plot is slightly more complicated way to determine the degree of similarity of interests of people gives Pearson's correlation coefficient. The correlation coefficient is a measure of how well the two data sets fit a straight line. The formula is more complicated than for the calculation of Euclidean distance, but it gives better results when the data is poorly normalized, for example, if some critics consistently exhibited films lower ratings than the national average.

From the above scatter plot the best coefficient of correlation that I have estimated is r = -.40, which shows weak negative correlation from two variable factors.

Question No 4

Having a sample of 5,000 is not necessarily better than having a sample of 500. How would you react to this statement? Support your answer with suitable examples and supportive references.

Sampling is one of the best techniques to assess the behavior of a large population. Systematic sampling is easier to perform in the field and provides a useful alternative to simple random sampling. The researcher starts at a random point and selects items that are a fixed distance apart. When no list of the population exists or if a list is in approximately random order, systematic sampling is often used as a proxy for simple random sampling. In cases in which the population is listed in a monotone order, systematic sampling usually results in estimators with smaller (though sometimes un-estimable) variances than those of simple random sampling. Repeated systematic sampling consists of more than one systematic sample, each with a different random starting point. Using the variability in the subsample means, one can get a measure of the variance of that estimate in the entire sample. When the population is in periodic order, then it is important to choose the period appropriately in order to get a representative sample.

One can classify systematic sampling as a special case of cluster sampling. The population is partitioned into clusters such that the clusters consist of units that are not contiguous. For systematic sampling to be effective, the ideal cluster should contain the full diversity of the population and thus be representative of the population. One simple example for systematic sampling is to interview subjects in a long queue about their ...

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