832 CHAPTER 12 Statistics + 4: LinReg (ax b). Then press ENTER twice. You will get r .921927852, = which represents the correlation coefficient. On the screen, you will also see values for a and b. Note that a represents the slope and b represents the y-coordinate of the y-intercept of the equation of the line of best fit. Thus, the slope is 3.229813665 and the y-coordinate of the y-intercept is 8.51552795. StatCrunch (available in MyLab Math and separately) To compute this line of best fit, start by entering the data (see Step 1 in the Technology Tip on page 791). 1. Enter the values for x under var 1 and the values for y under var 2. 2. Click Stat in the top menu. Select Regression then Simple Linear from the dropdown menu. 3. You will see the equation of the line of best fit written as var 2 8.515528 3.2298137 = + var 1. You will also see r (correlation coefficient) 0.92192785. = If you click on the arrow at the bottom of the results window, you will see the scatterplot with the graph of the line of best fit. There’s an App for That! Many of the concepts that we discuss throughout this section and throughout this entire chapter can be further explored with the use of an app on your smartphone or tablet computer. Several of these apps allow you to calculate the linear correlation coefficient and the equation of the line of best fit and allow you to estimate the predicted value of y from the line of best fit. As always, consult with your instructor before using these apps when completing work related to your course. Exercises Warm Up Exercises In Exercises 1– 6, fill in the blank with an appropriate word, phrase, or symbol(s). 1. A unitless measure that describes the strength of the linear relationship between two variables is called the linear correlation _________. Coefficient 2. The process of determining the linear relationship between two variables is called linear _________. Regression 3. a) The value of r, the linear correlation coefficient, that represents the strongest positive correlation between two variables is _________. 1 b) The value of r, the linear correlation coefficient, that represents the strongest negative correlation between two variables is _________. 1− c) The value of r, the linear correlation coefficient, that represents no correlation between two variables is _________. 0 4. If one quantity increases as the other quantity decreases, the two variables are said to have a(n) _________ correlation. Negative 5. If one quantity increases as the other quantity increases, the two variables are said to have a(n) _________ correlation. Positive 6. A plot of data points is called a(n) _________ diagram. Scatter In Exercises 7–10, indicate if you believe that a correlation exists between the quantities on the horizontal and vertical axes. If so, indicate if you believe that the correlation is a strong positive correlation, a strong negative correlation, a weak positive correlation, a weak negative correlation, or no correlation. Explain your answer. 7. y x No correlation 8. y x Weak negative correlation 9. y x Strong positive correlation 10. y x Strong negative correlation SECTION 12.6 Instructor Resources for Section 12.6 in MyLab Math • Objective-Level Videos 12.6 • Animation: Correlation and Regression • PowerPoint Lecture Slides 12.6 • MyLab Exercises and Assignments 12.6 • Chapter 12 Projects
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