These study tips are designed to clarify key points and help you to avoid errors that students commonly make. Review the Tips for Success as you study each chapter and review them again after you have studied each chapter.
- Be sure you have fully mastered the material on correlation in Chapter 11 before reading this chapter.
- When drawing a scatter diagram, to help you remember which variable goes on which axis, use the mnemonic "what’s known forms a stable basis for what’s predicted or envisioned up high".
- You can check the accuracy of your line on a scatter diagram by finding any third point. It should also fall on the line.
- Remember, the regression line is a visual equivalent of the linear prediction rule.
- You may have noticed that the formula for b is similar to the formula for the correlation coefficient, r, from Chapter 11. Be sure to use the appropriate formula for each statistic. The numerators of the two formulas are indeed the same (both are the sum of the products of the deviation scores), but the denominators are different.
- The β (beta) which is the standardized regression coefficient is entirely separate from the beta you learned about in Chapter 6. In that chapter, beta referred to the probability of making a Type II error – the probability of not getting a significant result, when the research hypothesis is true. Also, note that the use of the term β for the standardized regression coefficient is an exception to the rule that Greek letters refer to population parameters.
- The square root of the proportionate reduction in error should equal the correlation. In the problem on page 532, the square root of .82 = -.91 (it is a negative correlation in this example, as low scores go with high scores and highs with lows), which is consistent (allowing for rounding error) with the correlation we began with of -.90.
