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b.Here are the values of xlog(x) and ylog(y):x0.701.001.181.301.401.481.651.78y1.210.990.910.620.530.460.280.11Construct a scatterplot of these transformed data, andcomment on the pattern.c.Based on the accompanying MINITAB output, does theleast-squares line effectively summarize the relationshipbetween yand x?The regression equation islog(moisture) = 2.02 – 1.05 log(time)PredictorCoefSE CoefTPConstant2.017800.0958421.050.000log(time)–1.051710.07091–14.830.000S = 0.0657067R-Sq = 97.3%R-Sq(adj) = 96.9%Analysis of VarianceSourceDFSSMSFPRegression10.949780.94978219.990.000Residual Error60.025900.00432Total70.97569d.Use the MINITAB output to predict moisture contentwhen frying time is 35 sec.e.Do you think that predictions of moisture content usingthe model in Part (c) will be better than those using themodel fit in Example 5.16, which used transformed yval-ues but did not transform x?Explain.5.53● ▼The report “Older Driver Involvement in InjuryCrashes in Texas” (Texas Transportation Institute, 2004)included a scatterplot of yfatality rate (percentage ofdrivers killed in injury crashes) versus xdriver age. Theaccompanying data are approximate values read from thescatterplot.FatalityFatalityAgeRateAgeRate400.75802.20450.75853.00500.95903.20551.05a.Construct a scatterplot of these data.b.Using Table 5.5 and the ladder of transformations inFigure 5.31, suggest a transformation that might result invariables for which the scatterplot would exhibit a patternthat was more nearly linear.c. Reexpress xand/or yusing the transformation you rec-ommended in Part (b). Construct a scatterplot of the trans-formed data.252C h a p t e r 5■Summarizing Bivariate DataThe corresponding least-squares line isThis transformation can be reversed by squaring both sides to obtain an equation ofthe form ysome function of x:Since y2yand we get■ yˆ12.453.721x22x¿1xyˆ¿212.453.72x¿22yˆ¿2.453.72x¿..............................................................................................................Boldexercises answered in back●Data set available online but not required▼Video solution available
d.Does the scatterplot in Part (c) suggest that the trans-formation was successful in straightening the plot?e.Using the transformed variables, fit the least-squaresline and use it to predict the fatality rate for 78-year-olddrivers.5.54● The paper “Aspects of Food Finding by WinteringBald Eagles” (The Auk: 477–484) examined therelationship between the time that eagles spend aeriallysearching for food (indicated by the percentage of eaglessoaring) and relative food availability. The accompanyingdata were taken from a scatterplot that appeared in this pa-per. Let xdenote salmon availability and ydenote the per-centage of eagles in the air.x000.20.50.51.0y28.269.027.038.548.431.1x22.214.171.124.34.76.5y126.96.36.199.47.06.8a.Draw a scatterplot for this data set. Would you describethe plot as linear or curved?b.One possible transformation that might lead to astraighter plot involves taking the square root of both the xand yvalues. Use Figure 5.31 to explain why this mightbe a reasonable transformation.