if the range of one or both variables is restricted, the resulting correlation coefficient will likely: a.be decreased b. be increased c. remain the same d. either increase or decrease depending on the calculations. i chose c
disagree.
If the range of one or both variables is restricted, the resulting correlation coefficient will likely be decreased (option a). This is because a restricted range can limit the variability of the data, leading to a weaker relationship between the variables and a lower correlation coefficient.
To determine the probable effect of restricting the range of one or both variables on the resulting correlation coefficient, we need to understand how the correlation coefficient is calculated.
The correlation coefficient, denoted by "r," measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation.
When the range of one or both variables is restricted, it means that some values are excluded from the analysis. This restriction can affect the correlation coefficient in different ways.
If the restricted range includes extreme values or outliers that have a large influence on the data, restricting the range can help remove these outliers, consequently reducing the impact of those extreme values on the correlation coefficient. In this case, choosing option "a. be decreased" would be correct.
On the other hand, if the restricted range excludes the data points with high correlation, the correlation coefficient may increase. This can happen when the excluded values disproportionately affect the direction or strength of the relationship between the variables. In this scenario, option "b. be increased" would be the correct answer.
However, without specific information about the nature of the restrictions or the data itself, it is difficult to definitively state whether the correlation coefficient will increase, decrease, or remain unchanged. Thus, the most accurate answer would be "d. either increase or decrease depending on the calculations."