The linear correlation coefficient is also referred to as Pearson’s product moment correlation coefficient in honor of Karl Pearson, who originally developed it. The sample size is n.Īn alternate computation of the correlation coefficient is: Where x̄ and s x are the sample mean and sample standard deviation of the x’s, and ȳ and s y are the mean and standard deviation of the y’s. To quantify the strength and direction of the relationship between two variables, we use the linear correlation coefficient: Linear Correlation Coefficientīecause visual examinations are largely subjective, we need a more precise and objective measure to define the correlation between the two variables. When one variable changes, it does not influence the other variable. When two variables have no relationship, there is no straight-line relationship or non-linear relationship. For example, as age increases height increases up to a point then levels off after reaching a maximum height. Non-linear relationships have an apparent pattern, just not linear. Scatterplot of temperature versus wind speed. For example, as wind speed increases, wind chill temperature decreases. Negative relationships have points that decline downward to the right. For example, when studying plants, height typically increases as diameter increases. Positive relationships have points that incline upwards to the right. Linear relationships can be either positive or negative. This is the relationship that we will examine. A relationship is linear when the points on a scatterplot follow a somewhat straight line pattern.
For example, we measure precipitation and plant growth, or number of young with nesting habitat, or soil erosion and volume of water. In many studies, we measure more than one variable for each individual.