Final answer:
To determine if there is a linear relationship between the number of chicken pox cases and the years after 1988, one must assess if there's a consistent upward or downward trend in the scatter plot. If the pattern is non-linear, as it was with flu cases that initially increased and then consistently declined, a linear regression model would not be appropriate. Moreover, correlation does not imply causation, making it crucial to analyze the nature of the data.
Step-by-step explanation:
Examining the scatter plot and the number of chicken pox cases after 1988 with the variable x representing the number of years after 1988, and the variable y representing the number of cases in thousands, it is important to determine if there is a linear relationship present. The question of whether there is a linear relationship in the data relating to the number of chicken pox cases after 1988 requires us to look for a pattern in the scatter plot. If cases declined consistently over the years, we might establish a negative correlation, whereas an increase would suggest a positive correlation. However, if from a certain point onwards the number of cases stopped following a consistent trend up or down (as it happened with flu cases which increased until 1993 and then declined), then it would not be appropriate to use linear regression. Gathered evidence suggests that for determining the nature of the relationship, it is critical to consider whether the data demonstrates a clear upward or downward trend and whether any line could reasonably fit the majority of data points. Given that for flu cases an increase was followed by a consistent decline, making the pattern non-linear over the extended period, a linear model would not be the best fit. Thus, for the scatter plot concerning the number of chicken pox cases, if it demonstrates a similar pattern as flu cases, with an initial increase and then a decrease, the data would not be a good candidate for linear regression. Similarly, the absence of a linear pattern would indicate that it is not suitable to calculate a linear correlation coefficient. It's important to remember that correlation does not imply causation, so even when a linear association exists, we cannot confirm that one variable directly causes changes in another.