MODEL HOW TWO VARIABLES ARE RELATEDA regression line is a straight line that predicts the value of a response variable ‘y’ from the value of an explanatory variable ‘x’. The correlation is a summary measure of association. The regression line uses the following formula:The data is plotted before a regression line is made, because it can be strongly influenced by outliers. The regression equation is often called a prediction equation. The difference between y - ŷ, between an observed outcome y and its predicted value ŷ is the prediction error, called the residual. The average of the residuals is zero. The regression line has a smaller sum of squared residuals than any other line. It is called the least squares line. The population regression equation has the following formula:This formula is a model. A model is a simple approximation for how variables relate in a population. The probability distributions of y values at a fixed value of x is a conditional distribution (e.g: the means of annual income for people with 12 years of education).DESCRIBE STRENGTH OF ASSOCIATIONCorrelation does not differentiate between response and explanatory variables. The formula for the slope uses the correlation and can be calculated as following:Using this formula, the y-intercept can be calculated:The slope can’t be used to determine the strength of the association, because it determines on the units of measurement. The correlation is the standardized version of the slope. The formula for the correlation is the following:A property of the correlation is that at any particular x value, the predicated value of y is relatively closer to its mean than x is to its mean. If a particular ‘x’ value falls 2.0 standard deviations from the mean with a correlation of 0.80, then the predicted ‘y’ is ‘r’ times that many standard deviations from its mean, so the predicted ‘y’ would be 0.80 times 2.0 standard deviations from the mean. The predicted ‘y’ is...