There is a table of AVERAGE monthly temperatures of two different areas of the same city.
A scatterplot of the data is made to show that the relationship is linear between the two.
If raw data was used instead of the averages to make the scatterplot, the correlation coefficient would most likely:
The answer is decrease, but I'm not exactly sure why.
Within each month, there is more variation in terms of the daily temps.
To understand why the correlation coefficient would most likely decrease when raw data is used instead of averages, let's start by understanding what the correlation coefficient represents.
The correlation coefficient, typically denoted as 'r', measures the strength and direction of the linear relationship between two variables. It ranges between -1 and +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
In this case, we have a table of average monthly temperatures for two different areas of the same city. When calculating the average, we are essentially aggregating and summarizing the data to display a single value. By using averages, we remove some of the variability present in the raw data.
When raw data is used, each individual data point represents a specific measurement for a specific month in the respective areas. Since there can be variability in monthly temperatures, there might be some differences between individual data points from the same area. These differences can introduce noise or randomness into the data.
By taking the averages, we dampen the effect of individual fluctuations and obtain a smoother representation of the relationship between the two areas. When plotting the scatterplot using averages, any outliers or extreme values are likely to be mitigated to some extent.
Therefore, when raw data is used instead of averages, the correlation coefficient is more likely to decrease because the noise or variability in individual measurements can weaken the linearity of the relationship between the two areas. This decrease in correlation coefficient indicates that the relationship between the variables may not be as strong as when averages are used.
It's important to note that the exact impact on the correlation coefficient would depend on the characteristics of the data and the patterns present in it.