The accompanying data are the number of wins and the earned run averages (mean n

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 EEB Click the icon to view the table of numbers of wins and earned run average (b) x 10 wins (c) x = 21 wins (d) x=15wins The equation of the regression line is y (Round to two decimal places as needed.) Construct a scatter plot of the data and draw the regression li OA. Wins and ERA ERA ERA Earned run average, y 2.73 3.38 2.65 3.82 3.94 4.42 3.78 5.05 Wins, x 20 18 17 16 2 2 12 18 24 Wins 12 18 24 Wins (a) Predict the ERA for 5 wins, if it is meaningful. Select the within your choice 12 A y(Round to two decimal places as needed.) O B. It is not meaningful to predict this value of y because 9 C. It is not meaningful to predict this value of y because (b) Predict the ERA for 10 wins, if it is meaningful. Select the x within your choice Print Done 0 A, y = (Round to two decimal places as needed.) O B. It is not meaningful to predict this value of y because x 10 is inside the range of the original data. ° C. It is not meaningful to predict this value of y because x-10 is not an x-value in the original data (c) Predict the ERA for 21 wins, if it is meaningful. Select the correct choice below and, if necessary, fill in the answer box within your choice

Explanation / Answer

Formula for linear regression is

Y=a+bx

=.1857x+6.437

A)

For x=5

Y= (-0.1857*5)+ 6.437

=5.51

b)

For X=10

Y= (-0.1857*10)+ 6.437

=4.58

C)

For X=21

Y= (-0.1857*21)+ 6.437

=2.54

D)

For X=15

Y= (-0.1857*21)+ 6.437

Y= 3.65

Explanation

Linear regression formula

Y=a+bx

Y= dependent variable

a= y intercept

b=slope

Formula for calculating slope

b= r. (standard deviation of Y/standard deviation of x)

r is pearson’s correlation coefficient

r= sum

Formula for calculating a i.e y intercept

a=mean of y-slope.mean of x sample

First we need to calculate r

From using formula value of r= -0.8689

Average X value=14.625, Stdev X value=3.72125

Average Y value=3.777282, Stdev y value=0.807243

Thus by putting value of r in slope formulae

Slope=

b= r. (standard deviation of Y/standard deviation of x)

   =-0.8689(0.807243/3.777282

   = -0.185693

Intercept

a=mean of y-slope.mean of x sample

=3.777282-(-0.185693.14.625)

=3.777282+2.71

=6.43

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