# Linear regression, Pearson correlation coefficient, predict

Brian, this is Bernice. I have three questions that I hope you can help me with. I have retired from WCCCD, so I am using my personal email address. I hope you can help.

1. What is simple linear regression, and why is it useful? How would we predict a raw score from a raw score? What is the difference between the intercept and the slope? Why do we calculate them in simple linear regression?

2. What are three characteristics of the correlation coefficient? What is the difference between a positive and a negative correlation? How can we know if a certain correlation is a strong correlation?

3. How do we calculate the Pearson correlation coefficient?

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#### Solution Preview

1. Simple linear regression (SLR) is the most straightforward and popular regression technique because there is only one independent variable and the model is linear in both the independent variable and in the parameters. SLR is useful because the model can be used for making predictions. The prediction can be made because if you did a scatter plot of the data that was collected, you would then make a best fit straight line, and that straight line would let you estimate what y would be for a given x. The fact that you get an equation of a line in the form of y=mx+b, where m is the slope and b is the y-intercept, let's you estimate values from a raw score. The intercept will give you the point where the line crosses the y-axis and the slope will give you the direction in which the line ...