Which of the following values best represents the Pearson correlation for the data in the following scatterplot?

Question

BlackTom AI · Accepted Answer

First, restating the scenario: the question asks which value best represents the Pearson correlation for the data shown in the scatterplot. The provided answer option is A. 0.70, and the other options are B. 0.05, C. -0.05, and D. -0.70.

Option A (0.70): In a scatterplot where points trend upward from left to right in a fairly tight, linear fashion, the Pearson correlation coefficient is positive and relatively strong. A value around 0.7 indicates a strong positive linear relationship, which aligns with a clear upward pattern where high X values tend to accompany high Y values and there is less scatter around an approximate line.

Option B (0.05): A correlation near zero would imply almost no linear relationship between X and Y, with points scattered in no discernible linear pattern. The scatterplot, however, shows a discernible upward trend, so a near-zero value would be inconsistent with what’s visually suggested.

Option C (-0.05): A small negative value would indicate a slight inverse linear relationship—when X increases, Y tends to decrease slightly. This contradicts the observed upward trend where increases in X appear to be associated with increases in Y.

Option D (-0.70): A strong negative relationship would imply that as X increases, Y decreases in a fairly consistent manner. The plotted points do not show a downward pattern; instead, they tend to rise together, so a strong negative correlation would mischaracterize the direction of the trend.

In summary, the scatterplot displays a clear positive linear association with relatively limited dispersion around an upward path, which is best captured by a moderately strong positive correlation like 0.70. The other values either imply no linear relationship, the wrong direction, or a weaker/stronger magnitude than what the pattern suggests.

Which of the following values best represents the Pearson correlation for the data in the following scatterplot? 单项选择题

类似问题

A researcher is interested in examining the relationship between the number of bears in an area (Y) and its human population (X). The scatterplot of the data is reproduced below. This scatterplot would suggest that the correlation (Pearson’s r) for this distribution would be: