The scatterplot above shows a set of data values as well as a trend line for the data. Based on the trend line, which of the following best describes the relationship between x and y?
As x increases by 8, y tends to decrease by 6.
The trend line on the scatterplot indicates a negative correlation between x and y, suggesting that as the value of x increases, y consistently decreases. This specific decline is quantified by the slope of the trend line, which shows a decrease of 6 units in y for every 8 units increase in x.
This option accurately reflects the trend indicated by the scatterplot's trend line. The negative slope indicates that for every increase of 8 in x, there is a corresponding decrease of 6 in y, confirming the observed relationship in the data.
This choice suggests a smaller decrease in y compared to what is shown in the trend line. The trend line indicates a steeper negative slope, meaning that y decreases more significantly than just 4 units as x increases by 8.
Similar to option B, this choice underestimates the change in y. The data clearly shows that the decrease is more pronounced, with the trend line indicating a decrease of 6 in y for every increase of 8 in x, not just 2.
This statement contradicts the downward trend visible in the scatterplot. The trend line illustrates that y does not remain constant; rather, it shows a clear decrease as x increases, indicating a dynamic relationship.
This option suggests a positive correlation, which is entirely incorrect based on the data. The trend line reflects a negative slope, meaning that y decreases rather than increases as x rises.
The scatterplot illustrates a negative correlation between x and y, with the trend line revealing that for every increase of 8 in x, y decreases by 6. The other options misrepresent the relationship, either by suggesting a lesser decrease, a constant value, or an increase, all of which do not align with the data's trend. Understanding this relationship is crucial for accurately interpreting data trends in various analytical contexts.
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