Questions: Linear Models, Correlation, and Regression Worksheet 1. In baseball, a pitcher's Earned Run Average (ERA) is the average of earned runs given up by a pitcher per nine innings pitched. Strikeouts (SO) occur when a batter racks up three strikes during a time at bat. The data below shows Justin Verlander's ERA and number of SO during the time he pitched for the Detroit Tigers (2005-2017). ERA, x SO, y (x, y) 7.15 7 (7.15,7) 3.63 124 (3.63,124) 3.66 183 (3.66,183) 4.84 163 (4.84,163) 3.45 269 (3.45,269) 3.37 219 (3.37,219) 2.40 250 (2.40,250) 2.64 239 (2.64,239) 3.46 217 (3.46,217) 4.54 159 (4.54,159) 3.38 113 (3.38,113) 3.04 254 (3.04,254) 3.82 176 (3.82,176) a. Plot the data. b. Draw a line to best fit the data.

Linear Models, Correlation, and Regression Worksheet 1. In baseball, a pitcher's Earned Run Average (ERA) is the average of earned runs given up by a pitcher per nine innings pitched. Strikeouts (SO) occur when a batter racks up three strikes during a time at bat. The data below shows Justin Verlander's ERA and number of SO during the time he pitched for the Detroit Tigers (2005-2017). ERA, x SO, y (x, y) 7.15 7 (7.15,7) 3.63 124 (3.63,124) 3.66 183 (3.66,183) 4.84 163 (4.84,163) 3.45 269 (3.45,269) 3.37 219 (3.37,219) 2.40 250 (2.40,250) 2.64 239 (2.64,239) 3.46 217 (3.46,217) 4.54 159 (4.54,159) 3.38 113 (3.38,113) 3.04 254 (3.04,254) 3.82 176 (3.82,176) a. Plot the data. b. Draw a line to best fit the data.
Transcript text: Linear Models, Correlation, and Regression Worksheet 1. In baseball, a pitcher's Earned Run Average (ERA) is the average of earned runs given up by a pitcher per nine innings pitched. Strikeouts (SO) occur when a batter racks up three strikes during a time at bat. The data below shows Justin Verlander's ERA and number of SO during the time he pitched for the Detroit Tigers (2005-2017). ERA, $x$ & SO, $y$ & $(x, y)$ 7.15 & 7 & $(7.15,7)$ 3.63 & 124 & $(3.63,124)$ 3.66 & 183 & $(3.66,183)$ 4.84 & 163 & $(4.84,163)$ 3.45 & 269 & $(3.45,269)$ 3.37 & 219 & $(3.37,219)$ 2.40 & 250 & $(2.40,250)$ 2.64 & 239 & $(2.64,239)$ 3.46 & 217 & $(3.46,217)$ 4.54 & 159 & $(4.54,159)$ 3.38 & 113 & $(3.38,113)$ 3.04 & 254 & $(3.04,254)$ 3.82 & 176 & $(3.82,176)$ a. Plot the data. b. Draw a line to best fit the data.
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Solution

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Solution Steps

Step 1: Plot the Data
  • Plot the given data points (ERA, SO) on the provided graph.
  • The data points are:
    • (7.15, 7)
    • (3.63, 124)
    • (3.66, 183)
    • (3.45, 269)
    • (3.47, 250)
    • (2.40, 250)
    • (2.64, 219)
    • (3.46, 217)
    • (2.52, 250)
    • (3.82, 176)
Step 2: Draw a Line to Best Fit the Data
  • Draw a line that best fits the plotted data points.
  • The line should minimize the distance between the line and all the data points.

Final Answer

  • The data points are plotted on the graph.
  • A line of best fit is drawn through the data points.
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