A statistical program is recommended. Consider the following data for two variables, x and y. xi yi (a) Compute the stan
Posted: Tue Jul 05, 2022 9:56 am
A statistical program is recommended.
Consider the following data for twovariables, x and y.
xi
yi
(a)
Compute the standardized residuals for these data. (Round youranswers to two decimal places.)
xi
yi
Do the data include any outliers? Explain. (Round your answersto two decimal places.)
The standardized residual with the largest absolute valueis , correspondingto yi = . Since thisresidual is ---Select--- less than −2 between−2 and +2 greater than +2 ,it ---Select--- is definitely not couldbe an outlier.
(b)
Plot the standardized residuals against ŷ.
A standardized 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:Standardized Residuals. There is a horizontal line that spans thegraph at 0 on the vertical axis. There are 4 points below the lineand 3 points above it. The points are plotted from left to right inan upward, diagonal direction starting from the lower left cornerof the graph. Most of the points are between −0.9 to 0.3 onthe vertical axis; however, the maximum residual is atapproximately (136, 2.1).
A standardized 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:Standardized Residuals. There is a horizontal line that spans thegraph at 0 on the vertical axis. There are 4 points below the lineand 3 points above it. 6 of the points appear to vary randomlybetween −0.9 to 0.3 on the vertical axis; however, the maximumresidual is at approximately (119, 2.1).
A standardized 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:Standardized Residuals. There is a horizontal line that spans thegraph at 0 on the vertical axis. There are 3 points below the lineand 4 points above it. 6 of the points appear to vary randomlybetween −0.3 to 0.9 on the vertical axis; however, the minimumresidual is at approximately (119, −2.1).
A standardized 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:Standardized Residuals. There is a horizontal line that spans thegraph at 0 on the vertical axis. There are 4 points below the lineand 3 points above it. The points are plotted from left to right ina downward, diagonal direction starting from the upper left cornerof the graph. Most of the points are between −0.9 to 0.3 onthe vertical axis; however, the maximum residual is atapproximately (108, 2.1).
Does this plot reveal any outliers?
The plot shows no possible outliers.The plot shows one possibleoutlier. The plot shows two possibleoutliers.The plot shows more than two possible outliers.
(c)
Develop a scatter diagram for these data.
A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and islabeled: y. The points are plotted from left to rightin a downward, diagonal direction starting from the upper leftcorner of the diagram. The points are between 110 to 175 on thehorizontal axis and between 100 to 145 on the vertical axis. Thepoints are fairly scattered, though the second point from the leftis noticeably farther away from the others at 100 on the verticalaxis.
A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and islabeled: y. The points are plotted from left to rightin an upward, diagonal direction starting from the lower leftcorner of the diagram. The points are between 110 to 175 on thehorizontal axis and between 100 to 145 on the vertical axis. Thepoints are reasonably close together and each consecutive point ishigher than or just as high on the the diagram as the previouspoint.
A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and islabeled: y. The points are plotted from left to rightin an upward, diagonal direction starting from the lower leftcorner of the diagram. The points are between 110 to 175 on thehorizontal axis and between 100 to 145 on the vertical axis. Mostof the points are plotted reasonably close together, but the fourthpoint from the left is noticeably higher than the others at 145 onthe vertical axis.
A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and islabeled: y. The points are plotted from left to rightin a downward, diagonal direction starting from the upper leftcorner of the diagram. The points are between 110 to 175 on thehorizontal axis and between 100 to 145 on the vertical axis. Thepoints are fairly scattered, though the seventh point from left isslightly farther away from the others at 120 on the verticalaxis.
Does the scatter diagram indicate any outliers in the data?
The diagram indicates that there are no possible outliers.Thediagram indicates that there is one possibleoutlier. The diagram indicates that thereare two possible outliers.The diagram indicates that there are morethan two possible outliers.
In general, what implications does this finding have for simplelinear regression?
For simple linear regression, we can determine an outlier bylooking at the scatter diagram.For simple linear regression, wemust calculate standardized residuals, plot a standardized residualplot, and construct a scatter diagram to identify anoutlier. For simple linear regression,it is impossible to determine whether there is an outlier usingstandardized residuals, a standardized residual plot, or a scatterdiagram.
Consider the following data for twovariables, x and y.
xi
yi
(a)
Compute the standardized residuals for these data. (Round youranswers to two decimal places.)
xi
yi
Do the data include any outliers? Explain. (Round your answersto two decimal places.)
The standardized residual with the largest absolute valueis , correspondingto yi = . Since thisresidual is ---Select--- less than −2 between−2 and +2 greater than +2 ,it ---Select--- is definitely not couldbe an outlier.
(b)
Plot the standardized residuals against ŷ.
A standardized 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:Standardized Residuals. There is a horizontal line that spans thegraph at 0 on the vertical axis. There are 4 points below the lineand 3 points above it. The points are plotted from left to right inan upward, diagonal direction starting from the lower left cornerof the graph. Most of the points are between −0.9 to 0.3 onthe vertical axis; however, the maximum residual is atapproximately (136, 2.1).
A standardized 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:Standardized Residuals. There is a horizontal line that spans thegraph at 0 on the vertical axis. There are 4 points below the lineand 3 points above it. 6 of the points appear to vary randomlybetween −0.9 to 0.3 on the vertical axis; however, the maximumresidual is at approximately (119, 2.1).
A standardized 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:Standardized Residuals. There is a horizontal line that spans thegraph at 0 on the vertical axis. There are 3 points below the lineand 4 points above it. 6 of the points appear to vary randomlybetween −0.3 to 0.9 on the vertical axis; however, the minimumresidual is at approximately (119, −2.1).
A standardized 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:Standardized Residuals. There is a horizontal line that spans thegraph at 0 on the vertical axis. There are 4 points below the lineand 3 points above it. The points are plotted from left to right ina downward, diagonal direction starting from the upper left cornerof the graph. Most of the points are between −0.9 to 0.3 onthe vertical axis; however, the maximum residual is atapproximately (108, 2.1).
Does this plot reveal any outliers?
The plot shows no possible outliers.The plot shows one possibleoutlier. The plot shows two possibleoutliers.The plot shows more than two possible outliers.
(c)
Develop a scatter diagram for these data.
A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and islabeled: y. The points are plotted from left to rightin a downward, diagonal direction starting from the upper leftcorner of the diagram. The points are between 110 to 175 on thehorizontal axis and between 100 to 145 on the vertical axis. Thepoints are fairly scattered, though the second point from the leftis noticeably farther away from the others at 100 on the verticalaxis.
A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and islabeled: y. The points are plotted from left to rightin an upward, diagonal direction starting from the lower leftcorner of the diagram. The points are between 110 to 175 on thehorizontal axis and between 100 to 145 on the vertical axis. Thepoints are reasonably close together and each consecutive point ishigher than or just as high on the the diagram as the previouspoint.
A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and islabeled: y. The points are plotted from left to rightin an upward, diagonal direction starting from the lower leftcorner of the diagram. The points are between 110 to 175 on thehorizontal axis and between 100 to 145 on the vertical axis. Mostof the points are plotted reasonably close together, but the fourthpoint from the left is noticeably higher than the others at 145 onthe vertical axis.
A scatter diagram has 7 points plotted on it. The horizontalaxis ranges from 100 to 180 and is labeled: x. Thevertical axis ranges from 90 to 150 and islabeled: y. The points are plotted from left to rightin a downward, diagonal direction starting from the upper leftcorner of the diagram. The points are between 110 to 175 on thehorizontal axis and between 100 to 145 on the vertical axis. Thepoints are fairly scattered, though the seventh point from left isslightly farther away from the others at 120 on the verticalaxis.
Does the scatter diagram indicate any outliers in the data?
The diagram indicates that there are no possible outliers.Thediagram indicates that there is one possibleoutlier. The diagram indicates that thereare two possible outliers.The diagram indicates that there are morethan two possible outliers.
In general, what implications does this finding have for simplelinear regression?
For simple linear regression, we can determine an outlier bylooking at the scatter diagram.For simple linear regression, wemust calculate standardized residuals, plot a standardized residualplot, and construct a scatter diagram to identify anoutlier. For simple linear regression,it is impossible to determine whether there is an outlier usingstandardized residuals, a standardized residual plot, or a scatterdiagram.