Answer Happy

A statistical program is recommended. Consider the followingdata for two variables, x and y. xi 135 110 130 145 175 160 120 yi145 105 120 115 130 130 105 (a) Compute the standardized residualsfor these data. (Round your answers to two decimal places.) xi yiStandardized Residuals 135 145 110 105 130 120 145 115 175 130 160130 120 105 Do the data include any outliers? Explain. (Round youranswers to two decimal places.) The standardized residual with thelargest absolute value is , corresponding to yi = . Since thisresidual is ---Select--- , it ---Select--- an outlier. (b) Plot thestandardized residuals against ŷ. A standardized residual plot has7 points plotted on it. The horizontal axis ranges from 105 to 140and is labeled: y hat. The vertical axis ranges from −2.5 to 2.5and is labeled: Standardized Residuals. There is a horizontal linethat spans the graph at 0 on the vertical axis. There are 3 pointsbelow the line and 4 points above it. 6 of the points appear tovary randomly between −0.2 to 0.9 on the vertical axis; however,the minimum residual is at approximately (120, −2.1). Astandardized residual plot has 7 points plotted on it. Thehorizontal axis ranges from 105 to 140 and is labeled: y hat. Thevertical axis ranges from −2.5 to 2.5 and is labeled: StandardizedResiduals. There is a horizontal line that spans the graph at 0 onthe vertical axis. There are 4 points below the line and 3 pointsabove it. 6 of the points appear to vary randomly between −0.9 to0.2 on the vertical axis; however, the maximum residual is atapproximately (120, 2.1). A standardized residual plot has 7 pointsplotted on it. The horizontal axis ranges from 105 to 140 and islabeled: y hat. The vertical axis ranges from −2.5 to 2.5 and islabeled: Standardized Residuals. There is a horizontal line thatspans the graph at 0 on the vertical axis. There are 4 points belowthe line and 3 points above it. The points are plotted from left toright in a downward, diagonal direction starting from the upperleft corner of the graph. Most of the points are between −0.9 to0.2 on the vertical axis; however, the maximum residual is atapproximately (110, 2.1). A standardized residual plot has 7 pointsplotted on it. The horizontal axis ranges from 105 to 140 and islabeled: y hat. The vertical axis ranges from −2.5 to 2.5 and islabeled: Standardized Residuals. There is a horizontal line thatspans the graph at 0 on the vertical axis. There are 4 points belowthe line and 3 points above it. The points are plotted from left toright in an upward, diagonal direction starting from the lower leftcorner of the graph. Most of the points are between −0.9 to 0.2 onthe vertical axis; however, the maximum residual is atapproximately (135, 2.1). Does this plot reveal any outliers? Theplot shows no possible outliers. The plot shows one possibleoutlier. The plot shows two possible outliers. The plot shows morethan two possible outliers. (c) Develop a scatter diagram for thesedata. A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. The vertical axisranges from 90 to 150 and is labeled: y. The points are plottedfrom left to right in an upward, diagonal direction starting fromthe lower left corner of the diagram. The points are between 110 to175 on the horizontal axis and between 105 to 145 on the verticalaxis. The points are reasonably close together and each consecutivepoint is higher than or just as high on the the diagram as theprevious point. A scatter diagram has 7 points plotted on it. Thehorizontal axis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and is labeled: y. The pointsare plotted from left to right in a downward, diagonal directionstarting from the upper left corner of the diagram. The points arebetween 110 to 175 on the horizontal axis and between 105 to 145 onthe vertical axis. The points are fairly scattered, though theseventh point from left is slightly farther away from the others at120 on the vertical axis. A scatter diagram has 7 points plotted onit. The horizontal axis ranges from 100 to 180 and is labeled: x.The vertical axis ranges from 90 to 150 and is labeled: y. Thepoints are plotted from left to right in an upward, diagonaldirection starting from the lower left corner of the diagram. Thepoints are between 110 to 175 on the horizontal axis and between105 to 145 on the vertical axis. Most of the points are plottedreasonably close together, but the fourth point from the left isnoticeably higher than the others at 145 on the vertical axis. Ascatter diagram has 7 points plotted on it. The horizontal axisranges from 100 to 180 and is labeled: x. The vertical axis rangesfrom 90 to 150 and is labeled: y. The points are plotted from leftto right in a downward, diagonal direction starting from the upperleft corner of the diagram. The points are between 110 to 175 onthe horizontal axis and between 105 to 145 on the vertical axis.The points are fairly scattered, though the second point from theleft is noticeably farther away from the others at 105 on thevertical axis. Does the scatter diagram indicate any outliers inthe data? The diagram indicates that there are no possibleoutliers. The diagram indicates that there is one possible outlier.The diagram indicates that there are two possible outliers. Thediagram indicates that there are more than two possible outliers.In general, what implications does this finding have for simplelinear regression? For simple linear regression, we can determinean outlier by looking at the scatter diagram. For simple linearregression, it is impossible to determine whether there is anoutlier using standardized residuals, a standardized residual plot,or a scatter diagram. For simple linear regression, we mustcalculate standardized residuals, plot a standardized residualplot, and construct a scatter diagram to identify anoutlier.