494 CHAPTER 9 Correlation and Regression Extending Concepts Interchanging x and y In Exercises 31 and 32, perform the steps below. (a) Find the equation of the regression line for the data, letting Row 1 represent the x-values and Row 2 the y-values. Sketch a scatter plot of the data and draw the regression line. (b) Find the equation of the regression line for the data, letting Row 2 represent the x-values and Row 1 the y-values. Sketch a scatter plot of the data and draw the regression line. (c) Describe the effect of switching the explanatory and response variables on the regression line. 31. Row 1 0123355567 Row 2 96 85 82 74 95 68 76 84 58 65 32. Row 1 16 25 39 45 49 64 70 Row 2 109 122 143 132 199 185 199 Residual Plots A residual plot allows you to assess correlation data and check for possible problems with a regression model. To construct a residual plot, make a scatter plot of 1x, y - ny2, where y - ny is the residual of each y-value. If the resulting plot shows any type of pattern, then the regression line is not a good representation of the relationship between the two variables. If it does not show a pattern—that is, if the residuals fluctuate about 0—then the regression line is a good representation. Be aware that if a point on the residual plot appears to be outside the pattern of the other points, then it may be an outlier. In Exercises 33 and 34, (a) find the equation of the regression line, (b) construct a scatter plot of the data and draw the regression line, (c) construct a residual plot, and (d) determine whether there are any patterns in the residual plot and explain what they suggest about the relationship between the variables. 33. x 38 34 40 46 43 48 60 55 52 y 24 22 27 32 30 31 27 26 28 34. x 8 4157 6 312105 y 1811291814 8 252012 Influential Points An influential point is a point in a data set that can greatly affect the graph of a regression line. An outlier may or may not be an influential point. To determine whether a point is influential, find two regression lines: one including all the points in the data set, and the other excluding the possible influential point. If the slope or y-intercept of the regression line shows significant changes, then the point can be considered influential. An influential point can be removed from a data set only when there is proper justification. In Exercises 35 and 36, (a) construct a scatter plot of the data, (b) identify any possible outliers, and (c) determine whether the point is influential. Explain your reasoning. 35. x 5 6 9 1014171944 y 32332826252323 8
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