Answer Happy

Given are data for two variables, x and y. xi 6 11 15 18 20 yi 78 13 21 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 7 11 8 15 13 18 21 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 start above the line at x = 6 in the upperleft corner of the plot, then are plotted from left to right in adownward, diagonal direction until reaching a low below the line atx = 15. They then continue to be plotted in an upward diagonaldirection until reaching a high above the line at x = 20. Themaximum residual is located at x = 6. A residual plot has 5 pointsplotted on it. The horizontal axis ranges from 0 to 25 and islabeled: x. The vertical axis ranges from −6 to 6 and is labeled:Residuals. 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 start above the line at x = 6 in the upper left cornerof the 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 = 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 are plotted from left to right in an upward, diagonaldirection starting from the lower left corner of the plot. Theminimum residual is located at x = 6 and the maximum occurs 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 a downward, diagonal direction starting from the upperleft corner of the plot. The maximum residual is located at x = 6and the minimum occurs at x = 20. Do the assumptions about theerror terms seem to be satisfied? The plot suggests curvature inthe residuals indicating that the error term assumptions aresatisfied. The plot suggests curvature in the residuals indicatingthat the error term assumptions are not satisfied. The plotsuggests a generally horizontal band of residual points indicatingthat the error term assumptions are satisfied. The plot suggests agenerally horizontal band of residual points indicating that theerror term assumptions are not satisfied. The plot suggests afunnel pattern in the residuals indicating that the error termassumptions are not satisfied. (d) Compute the standardizedresiduals. (Round your answers to two decimal places.) xi yiStandardized Residuals 6 7 11 8 15 13 18 21 20 30 (e) Develop aplot of the standardized residuals against ŷ. A standardizedresidual plot has 5 points plotted on it. The horizontal axisranges from 0 to 30 and is labeled: y hat. The vertical axis rangesfrom −3 to 3 and is labeled: Standardized 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 about y hat = 3 in the upper left corner of theplot, then are plotted from left to right in a downward, diagonaldirection until reaching a low below the line at about y hat = 17.They then continue to be plotted in an upward diagonal directionuntil reaching a high above the line at about y hat = 25. 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 an upward, diagonaldirection starting from the lower left corner of the plot. Thepoints are between 3 to 26 on the horizontal axis and between −1.1to 1.5 on the vertical axis. 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 = 3 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. A standardized residual plothas 5 points plotted on it. The horizontal axis ranges from 0 to 30and is 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. 2 points lie above theline and 3 lie below it. The points are plotted from left to rightin a downward, diagonal direction starting from the upper leftcorner of the plot. The points are between 3 to 26 on thehorizontal axis and between −1.1 to 1.5 on the vertical axis. Whatconclusions can you draw from this plot? The standardized residualplot has the same shape as the original residual plot. The plotsuggests a generally horizontal band of residual points indicatingthat the error term assumptions are not satisfied. The standardizedresidual plot has a different shape than the original residualplot. The plot suggests curvature in the residuals indicating thatthe error term assumptions are satisfied. The standardized residualplot has a different shape than the original residual plot. Theplot suggests a generally horizontal band of residual pointsindicating that the error term assumptions are satisfied. Thestandardized residual plot has the same shape as the originalresidual plot. The plot suggests curvature in the residualsindicating that the error term assumptions are not satisfied. Thestandardized residual plot has a different shape than the originalresidual plot. The plot suggests a funnel pattern in the residualsindicating that the error term assumptions are notsatisfied.