# Linear relationship and the sample correlation coefficient

In which data set is there evidence of a strong nonlinear relationship between the two variables? (x,y u,v w,t m,n no data sets at all)

Which data set indicates the strongest positive linear relationship between its two variables? (x,y u,v w,t m,n)

Which data set has an apparent negative, but not perfect linear relationship between its two variables? (x,y u,v w,t m,n none of the data sets)

WHich data set indicates a perfect negative linear relationship between its two variables? (x,y u,v w,t m,n or none of the data sets)

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#### Solution Preview

Here are some basics about the correlation coefficient r: Correlation coefficient measures the strength and the direction of a linear relationship between two variables. r is always between -1 and 1, inclusive. The + and - signs are used for positive linear correlations and negative linear correlations, respectively. There are three types of correlation:

Positive correlation: If x and y have a strong positive linear correlation, r is close to +1. An r value of exactly +1 indicates a perfect positive fit. Positive values indicate a ...

#### Solution Summary

It explains the linear relationship and the sample correlation coefficient in detail.