Data were collected for a sample of companies regarding their investment in quality improvement efforts and cost savings realized as a result (both measured as a percentage of sales revenue). Below is the scatterplot. The correlation coefficient for these data is r = 0.913. If data were collected for individual departments within companies rather than at the company level, would you expect the correlation to be weaker, stronger or about the same? Explain.

Question

Data were collected for a sample of companies regarding their investment in quality improvement efforts and cost savings realized as a result (both measured as a percentage of sales revenue). Below is the scatterplot.  The correlation coefficient for these data is r = 0.913. If data were collected for individual departments within companies rather than at the company level, would you expect the correlation to be weaker, stronger or about the same? Explain.

Quizplus · Accepted Answer

The Answer is Relationships based on averages have higher correlation coefficients than relationships based on individual data. Therefore, a scatterplot of the investment and cost savings of quality improvement efforts for individual departments would show much more scatter and a weaker correlation coefficient.

Data Were Collected for a Sample of Companies Regarding Their