![]() Plugging the data into our Linear Regression Calculator we can see that the scatter-plot created with the data shows a strong positive relationship between the two scores. Then, using linear regression, we can predict the GPA of students at university based on their performance in high school. We will start with the assumption that high school GPA will correlate with higher university GPA performance. Let’s take a data set of high school and university GPA scores for a set of 105 computer science majors. Example of Linear RegressionĬonsider a real life example we took from the Online Stat Book. The value of \(r\) is unchanged if either \(X\) or \(Y\) is multiplied by a constant or if a constant is added. Correlation coefficient \(r\) is a measure of the linear association between the \(X\) and \(Y\) variables.Ħ. If \(r\) = 0, there is no linear relationship between the \(X\) and \(Y\) variables.ĥ. If \(r\) = -1, the data points fall on a straight line with negative slope.Ĥ. If \(r\) = 1, the data points fall on a straight line with positive slope.ģ. The range of \(r\) is between -1 and 1, inclusive.Ģ. The correlation coefficient has the following characteristics.ġ. Solving this system gives us the parameters \(a\) and \(b\): This leads to a system of two linear equations in two variables. The minimum condition for the sum of squared offsets is the equality to zero of the derivatives of this sum with respect to the parameters of the approximating line. The Linear Least Squares Regression Line method is a mathematical procedure for finding the best fit of a straight line to a given set of points by minimizing the sum of the squares of the point offsets from the approximating line. ![]()
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