Given are data for two variables, x and y. xi 6 11 15 18 20 yi 5 7 13 20 30 (a) Develop an estimated regression equation

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Given are data for two variables, x and y. xi 6 11 15 18 20 yi 57 13 20 30 (a) Develop an estimated regression equation for thesedata. (Round your numerical values to two decimal places.) ŷ = (b)Compute the residuals. (Round your answers to two decimal places.)xi yi Residuals 6 5 11 7 15 13 18 20 20 30 (c) Develop a plot ofthe residuals against the independent variable x. A residual plothas 5 points plotted on it. The horizontal axis ranges from 0 to 25and is labeled: x. The vertical axis ranges from −6 to 6 and islabeled: Residuals. There is a horizontal line that spans the graphat 0 on the vertical axis. 2 points lie above the line and 3 liebelow it. The points are plotted from left to right in a downward,diagonal direction starting from the upper left corner of the plot.The maximum residual is located at x = 6 and the minimum occurs atx = 20. A residual plot has 5 points plotted on it. The horizontalaxis ranges from 0 to 25 and is labeled: x. The vertical axisranges from −6 to 6 and is labeled: Residuals. There is ahorizontal line that spans the graph at 0 on the vertical axis. 2points lie above the line and 3 lie below it. The points startabove the line at x = 6 in the upper left corner of the plot, thenare plotted from left to right in a downward, diagonal directionuntil reaching a low below the line at x = 15. They then continueto be plotted in an upward diagonal direction until reaching a highabove the line at x = 20. The maximum residual is located at x =20. A residual plot has 5 points plotted on it. The horizontal axisranges from 0 to 25 and is labeled: x. The vertical axis rangesfrom −6 to 6 and is labeled: Residuals. There is a horizontal linethat spans the graph at 0 on the vertical axis. 2 points lie abovethe line and 3 lie below it. The points are plotted from left toright in an upward, diagonal direction starting from the lower leftcorner of the plot. The minimum residual is located at x = 6 andthe maximum occurs at x = 20. A residual plot has 5 points plottedon it. The horizontal axis ranges from 0 to 25 and is labeled: x.The vertical axis ranges from −6 to 6 and is labeled: Residuals.There is a horizontal line that spans the graph at 0 on thevertical axis. 2 points lie above the line and 3 lie below it. Thepoints start above the line at x = 6 in the upper left corner ofthe plot, then are plotted from left to right in a downward,diagonal direction until reaching a low below the line at x = 15.They then continue to be plotted in an upward diagonal directionuntil reaching a high above the line at x = 20. The maximumresidual is located at x = 6. Do the assumptions about the errorterms seem to be satisfied? The plot suggests a funnel pattern inthe residuals indicating that the error term assumptions are notsatisfied. The plot suggests curvature in the residuals indicatingthat the error term assumptions are satisfied. The plot suggestscurvature in the residuals indicating that the error termassumptions are not satisfied. The plot suggests a generallyhorizontal band of residual points indicating that the error termassumptions are satisfied. The plot suggests a generally horizontalband of residual points indicating that the error term assumptionsare not satisfied. (d) Compute the standardized residuals. (Roundyour answers to two decimal places.) xi yi Standardized Residuals 65 11 7 15 13 18 20 20 30 (e) Develop a plot of the standardizedresiduals against ŷ. A standardized residual plot has 5 pointsplotted on it. The horizontal axis ranges from 0 to 30 and islabeled: y hat. The vertical axis ranges from −3 to 3 and islabeled: Standardized Residuals. There is a horizontal line thatspans the graph at 0 on the vertical axis. 2 points lie above theline and 3 lie below it. The points are plotted from left to rightin an upward, diagonal direction starting from the lower leftcorner of the plot. The points are between 1 to 26 on thehorizontal axis and between −1 to 1.6 on the vertical axis. Astandardized residual plot has 5 points plotted on it. Thehorizontal axis ranges from 0 to 30 and is labeled: y hat. Thevertical axis ranges from −3 to 3 and is labeled: StandardizedResiduals. There is a horizontal line that spans the graph at 0 onthe vertical axis. 2 points lie above the line and 3 lie below it.The points are plotted from left to right in a downward, diagonaldirection starting from the upper left corner of the plot. Thepoints are between 1 to 26 on the horizontal axis and between −1 to1.6 on the vertical axis. A standardized residual plot has 5 pointsplotted on it. The horizontal axis ranges from 0 to 30 and islabeled: y hat. The vertical axis ranges from −3 to 3 and islabeled: Standardized Residuals. There is a horizontal line thatspans the graph at 0 on the vertical axis. 2 points lie above theline and 3 lie below it. The points start above the line at about yhat = 2 in the upper left corner of the plot, then are plotted fromleft to right in a downward, diagonal direction until reaching alow below the line at about y hat = 17. They then continue to beplotted in an upward diagonal direction until reaching a high abovethe line at about y hat = 25. A standardized residual plot has 5points plotted on it. The horizontal axis ranges from 0 to 30 andis labeled: y hat. The vertical axis ranges from −3 to 3 and islabeled: Standardized Residuals. There is a horizontal line thatspans the graph at 0 on the vertical axis. 3 points lie above theline and 2 lie below it. The points start below the line at about yhat = 2 in the lower left corner of the plot, then are plotted fromleft to right in an upward, diagonal direction until reaching ahigh above the line at about y hat = 17. They then continue to beplotted in a downward, diagonal direction until reaching a lowbelow the line at about y hat = 25. What conclusions can you drawfrom this plot? The standardized residual plot has a differentshape than the original residual plot. The plot suggests curvaturein the residuals indicating that the error term assumptions aresatisfied. The standardized residual plot has the same shape as theoriginal residual plot. The plot suggests curvature in theresiduals indicating that the error term assumptions are notsatisfied. The standardized residual plot has a different shapethan the original residual plot. The plot suggests a funnel patternin the residuals indicating that the error term assumptions are notsatisfied. The standardized residual plot has the same shape as theoriginal residual plot. The plot suggests a generally horizontalband of residual points indicating that the error term assumptionsare not satisfied. The standardized residual plot has a differentshape than the original residual plot. The plot suggests agenerally horizontal band of residual points indicating that theerror term assumptions are satisfied.