(1 point) The folowing data represents the winning percentage (the number of win
ID: 3313667 • Letter: #
Question
(1 point) The folowing data represents the winning percentage (the number of wins out of 162 games in a season) as well as the teams Eamed Run Average, or ERA ERA s a pitching statistic. The lower the ERA, the less runs an opponent wil score per game Smaler ERA's refect (0 a good petching stat and (u) a good team defense You are to investigate the relationship betwen a team's winning percentage Y, and es Eamed Run Average (ERA) . X 3 13 3.68 3.92 4.00 4.12 0 635802 0 518519 0.580247 0407407 0.462963 0.450617 0 487654 0 456790 0 574047 4 62 3.89 5.20 4.36 491 3.75 (a) Using MINITAB, create a scatter-plot of the data. What can you conciude trom this scatter-plot? A. There is a negative linear relationship between a teams winning percentage and tS ERA B. There is not a linear C. There is a po hip between the a teams winning and its ERAExplanation / Answer
a. Ans: Using MINITAB the Scatter plot is given by
From the Above scatter plot we see that as we increase X i.e ERA the variable Winning proportion i.e Y Decreases, so there is negative correlation between Y and X.
b. Ans:
Using MINITAB the least square estimate of the linear model is
y = 0.915 - 0.0964 x.
c. Ans:
Pearson correlation of y and x i.e, r = -0.686. so coefficient of determination is r2=0.4705. We conclude that the percentage of variation in dependent varaiable is 47% caused by independent variable.
d.Ans:
Slope is 0.0964. Thus we conclude that one Unit increase in ERA (x) variable will decrease 0.09..times Winning proportion i.e y.
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