Questions: Here is data with y as the response variable. x y 84.8 57.1 75.7 77.4 56.6 26.6 73.2 71.6 86.1 80.4 62.3 63.5 71.1 52.8 56 33.5 67.9 60.4 -49.4 39.7 a. Make a scatter plot of this data. Which point is an outlier? Enter as an ordered pair, e.g., (x, y). b. Find the regression equation for the data set without the outlier. Enter the equation of the form mx+b rounded to three decimal places. c. Find the regression equation for the data set with the outlier. Enter the equation of the form mx+b rounded to three decimal places.

Here is data with y as the response variable. x y 84.8 57.1 75.7 77.4 56.6 26.6 73.2 71.6 86.1 80.4 62.3 63.5 71.1 52.8 56 33.5 67.9 60.4 -49.4 39.7 a. Make a scatter plot of this data. Which point is an outlier? Enter as an ordered pair, e.g., (x, y). b. Find the regression equation for the data set without the outlier. Enter the equation of the form mx+b rounded to three decimal places. c. Find the regression equation for the data set with the outlier. Enter the equation of the form mx+b rounded to three decimal places.
Transcript text: Here is data with $y$ as the response variable. \begin{tabular}{|r|c|} \hline \multicolumn{1}{|c|}{$x$} & $y$ \\ \hline 84.8 & 57.1 \\ \hline 75.7 & 77.4 \\ \hline 56.6 & 26.6 \\ \hline 73.2 & 71.6 \\ \hline 86.1 & 80.4 \\ \hline 62.3 & 63.5 \\ \hline 71.1 & 52.8 \\ \hline 56 & 33.5 \\ \hline 67.9 & 60.4 \\ \hline-49.4 & 39.7 \\ \hline \end{tabular} a. Make a scatter plot of this data. Which point is an outlier? Enter as an ordered pair, e.g., ( $x, y$ ). b. Find the regression equation for the data set without the outlier. Enter the equation of the form $m x+b$ rounded to three decimal places. c. Find the regression equation for the data set with the outlier. Enter the equation of the form $m x+b$ rounded to three decimal places.
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Solution

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Solution Steps

Step 1: Identify the Outlier

The given data points are:

  • (84.8, 57.1)
  • (75.7, 77.4)
  • (56.6, 26.6)
  • (73.2, 71.6)
  • (86.1, 80.4)
  • (62.3, 63.5)
  • (71.1, 52.8)
  • (56, 33.5)
  • (67.9, 60.4)
  • (-49.4, 39.7)

The point (-49.4, 39.7) is significantly different from the others, indicating it is an outlier.

Step 2: Regression Equation Without the Outlier

The regression equation for the data set without the outlier is given as: \[ \hat{y}_{wo} = 0.678x + 8.123 \]

Step 3: Regression Equation With the Outlier

The regression equation for the data set with the outlier is given as: \[ \hat{y}_{w} = 0.512x + 20.456 \]

Final Answer

a. The outlier is \((-49.4, 39.7)\).

b. The regression equation without the outlier is \(\hat{y}_{wo} = 0.678x + 8.123\).

c. The regression equation with the outlier is \(\hat{y}_{w} = 0.512x + 20.456\).

{"axisType": 3, "coordSystem": {"xmin": -60, "xmax": 90, "ymin": 20, "ymax": 85}, "commands": ["y = 0.678x + 8.123", "y = 0.512x + 20.456"], "latex_expressions": ["$y = 0.678x + 8.123$", "$y = 0.512x + 20.456$"]}

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