Question at position 3 A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical plant. Varieties X and O are represented by x’s and o’s, respectively, in the following scatterplot. Which of the following statements is true? Considering both varieties together, the least-squares regression line for predicting sepal length from sepal width has a negative slope.Considering both varieties together, there is a negative correlation between sepal length and width.Considering Variety O only, the least-squares regression line for predicting sepal length from sepal width has a positive slope.Considering Variety X only, there is a positive correlation between sepal length and width.Considering each variety separately, there is a negative correlation between sepal length and width.

Question

Question at position 3 A study examined the relationship between the sepal length and sepal width for two varieties of an exotic tropical plant. Varieties X and O are represented by x’s and o’s, respectively, in the following scatterplot. Which of the following statements is true? Considering both varieties together, the least-squares regression line for predicting sepal length from sepal width has a negative slope.Considering both varieties together, there is a negative correlation between sepal length and width.Considering Variety O only, the least-squares regression line for predicting sepal length from sepal width has a positive slope.Considering Variety X only, there is a positive correlation between sepal length and width.Considering each variety separately, there is a negative correlation between sepal length and width.

BlackTom AI · Accepted Answer

To tackle this question, I’ll examine what each statement claims about the relationship between sepal length and width for the two varieties and for each variety separately.
Option 1: 'Considering both varieties together, the least-squares regression line for predicting sepal length from sepal width has a negative slope.' This would imply that, when pooling all data points from X and O, longer sepals tend to occur with smaller widths. However, looking at the scatterplot, the X points show a strong negative relationship (shorter widths with longer lengths) and the O points also show a negative relationship, but the overall combined pattern is not clearly aligned along a single negative regression line due to the two clusters being separated. So this statement is not reliably supported by the combined data.
Option 2: 'Considering both varieties together, there is a negative correlation between sepal length and width.' The plot displays two distinct clusters: one with small lengths and small widths (X) and one with larger lengths and larger widths (O). Each cluster individually shows a negative relation, but across both varieties together the data do not form a single elongated pattern; the two clusters may obscure or distort a simple negative correlation when pooled. Therefore, asserting a negative correlation for the combined data is questionable and likely incorrect.
Option 3: 'Considering Variety O only, the least-squares regression line for predicting sepal length from sepal width has a positive slope.' In Variety O (the higher-right cluster), as width increases, length also tends to increase, which would yield a positive slope in a regression of length on width. However, the typical interpretation for this cluster in the scatterplot is a positive association, not negative, so this statement is claiming the wrong direction if it’s describing the regression line; the slope appears positive, not negative.
Option 4: 'Considering Variety X only, there is a positive correlation between sepal length and width.' For Variety X (the lower-left cluster), as width increases, length tends to decrease, showing a negative association. Thus this statement is incorrect because it asserts a positive correlation where the data show the opposite.
Option 5: 'Considering each variety separately, there is a negative correlation between sepal length and width.' Observing the plot, each variety forms its own linear trend with a downward slope: larger widths correspond to shorter lengths within X, and larger widths (within the X-like region) also tend to correspond to shorter lengths; similarly, the O cluster shows that as width increases, length decreases. In both varieties individually, the pattern is negative, so this statement accurately describes both clusters when considered separately.
Putting it together, the most accurate interpretation aligns with the statement that, when you look at each variety separately, sepal length and width are negatively correlated. The other options either misstate the direction of the relationship for a given variety (options 3 and 4) or rely on the combined data producing a simple negative correlation or regression line that isn’t clearly supported by the plot (options 1 and 2).

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