Question

the accompanying data are the number of wins and the earned run averages (mean number of earned runs allowed per nine innings pitched) for eight baseball pitchers in a recent season. find the equation of the regression line. then construct a scatter plot of the data and draw the regression line. then use the regression equation to predict the value of y for each of the given x - values, if meaningful. if the x - value is not meaningful to predict the value of y, explain why not.
(a) ( x = 5 ) wins
(b) ( x = 10 ) wins
(c) ( x = 19 ) wins
(d) ( x = 15 ) wins
click the icon to view the table of numbers of wins and earned run average.
the equation of the regression line is ( hat{y}=-0.19x + 6.48 ).
(round to two decimal places as needed.)
construct a scatter plot of the data and draw the regression line. choose the correct graph below.
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Explanation:

The regression equation is given as $\hat{y} = -0.19x + 6.48$, where $x$ is wins and $y$ is ERA. We need to check which scatter plot shows a negative linear trend (since the slope is -0.19) with points roughly following a line with this slope.

• Option A: Shows a positive slope (line goes up from left to right) → Incorrect.
• Option B: Shows a vertical line → Incorrect (no linear trend with slope -0.19).
• Option C: Shows a negative slope (line goes down from left to right) → Matches the regression line's slope.
• Option D: Shows a non-linear pattern → Incorrect.

Answer:

C (the scatter plot with a negative-sloping regression line)