Getting SPSS to make a scatter plot and put a least squares regression line on our scatterplot What we want is the line (and linear equation) the fits the best. In fact it is not too hard to imagine several different possible lines fitting to this data. Clearly no single straight line will fit each data point (that is, you can't draw a single line through all of the data points). Now let's look at a case when the correlation is not perfect. There is only one possible line that makes sense to fit to this set of data. When we do a regression analysis, what we are doing is trying to find the line (and linear equation) that best fits the data points. Let's start with the case of a perfect positive correlation (r = 1.0). Okay, now let's return to our scatterplots. recall that predicting Y based on X is one of the main things that this chapter is all about In other words, using the linear equation, we can determine the value of Y, if we know the values of X, b, & a We can describe the line in the following linear equation:

The intercept (a) is the value of Y when X = 0. Let's start by reviewing some old geometry. Prediction - if we know that two variables are strongly related, then we may be able to predict the value of one, based on the value of the other.Į.g., if you know that ultrasound measurements of a baby's head are positively correlated with birth weight, then you can make an educated guess of the baby's birth weight by measuring the baby's head from an ultrasound Regression will give us these properties as well as allows us to make specific predictions about one variable, based on what we know about another variable. Regression allows one to predict scores on one variable given a score on anotherīoth correlation and regression test the null hypothesis that the two variables are independent of one anotherĪs we discussed last time, a correlation tells us about three characteristics about the relationship between X and Y Computing the residuals (error around the line)Ĭorrelation and regression procedures share a number of similarities.Ĭorrelation describes the relationship between two continuous variables.Computing the least squares regression line.The relationship between correlation and regression.

Linear regression equation example