What type of correlation does r = -0.3 indicate in a scatterplot?

Study for the HSC Mathematics Standard 2 Exam. Utilize flashcards and multiple choice questions, each with hints and explanations. Prepare confidently for your exam success!

When interpreting the value of the correlation coefficient ( r = -0.3 ), it is essential to understand the implications of the negative sign as well as the magnitude of the value. In this case, the negative sign indicates that there is an inverse relationship between the two variables being measured; as one variable increases, the other tends to decrease, albeit not in a strong or clear manner.

The number ( -0.3 ) suggests a low level of correlation. Correlation coefficients generally range from -1 to +1, with values closer to -1 indicating a strong negative correlation and values close to 0 implying little to no correlation. Thus, a value of ( -0.3 ) does not signify a robust relationship but indicates a weak negative correlation instead. Therefore, the characterization of this correlation as low negative is accurate, as it reflects a slight tendency for the variables to move in opposite directions.

This understanding helps in visualizing the scatterplot: points would be loosely scattered in a way that suggests a slight decrease in one variable as the other increases, but they are likely to be quite dispersed rather than forming a tight linear pattern.

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