# Relationship between correlation coefficient and slope of regression

### How does the correlation coefficient differ from regression slope? - Cross Validated

Correlation is a measure of association between two variables. When calculating a correlation coefficient for ordinal data, select Spearman's technique. For interval The slope and y intercept are incorporated into the regression equation. Is there a relationship between the correlation coefficient and the slope of a linear It is easiest to see the relationship for a regression with just one predictor. Correlation is a measure of the strength of a relationship between variables. The variables are The slope is always the coefficient of the x term in the equation.

In the case of the examples used here, the data were obtained by counting the breathing rate of goldfish in a laboratory experiment. Nature of data The data for regression and correlation consist of pairs in the form x,y. The independent variable x is determined by the experimenter.

This means that the experimenter has control over the variable during the experiment.

In our experiment, the temperature was controlled during the experiment. The dependent variable y is the effect that is observed during the experiment.

### Regression and Correlation

It is assumed that the values obtained for the dependent variable result from the changes in the independent variable. Regression and correlation analyses will determine the nature of this relationship, if any, and the strength of the relationship. It can be a consideration that all of the x,y pairs form a population.

The purpose of running the regression is to find a formula that fits the relationship between the two variables. Then you can use that formula to predict values for the dependent variable when only the independent variable is known.

## Pearson Correlation and Linear Regression

A doctor could prescribe the proper dose based on a person's body weight. The regression line known as the least squares line is a plot of the expected value of the dependent variable for all values of the independent variable. Technically, it is the line that "minimizes the squared residuals". The regression line is the one that best fits the data on a scatterplot.

Using the regression equation, the dependent variable may be predicted from the independent variable. Correlation does not fit a line through the data points. You simply are computing a correlation coefficient r that tells you how much one variable tends to change when the other one does. When r is 0. When r is positive, there is a trend that one variable goes up as the other one goes up.

When r is negative, there is a trend that one variable goes up as the other one goes down. Linear regression finds the best line that predicts Y from X. Correlation does not fit a line.

**Regression: Slope, intercept, and interpretation**

What kind of data? Correlation is almost always used when you measure both variables. It rarely is appropriate when one variable is something you experimentally manipulate.