Data were collected to explain the number of wins a major league baseball team has based on the earned run average (ERA) of the team’s starting pitchers g) What is the effect on wins of decreasing the ERA by 1 run?

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Data were collected to explain the number of wins a major league baseball team has based on the earned run average (ERA) of the team’s starting pitchers g) What is the effect on wins of decreasing the ERA by 1 run? *COMPLETE THE TABLE BELOW*
) What is the predicted number of wins for a team with an ERA of 3.50?
Regression tquation
y =I6S.46 -21.48X
Substitute X35
So ý = 165,46 -21, 48X =165,46 21,483,5=165,48 18
g) What is the effect on wins of decreasing the ERA by 1 run?
90,28
Transcribed Image Text:) What is the predicted number of wins for a team with an ERA of 3.50? Regression tquation y =I6S.46 -21.48X Substitute X35 So ý = 165,46 -21, 48X =165,46 21,483,5=165,48 18 g) What is the effect on wins of decreasing the ERA by 1 run? 90,28
5) Data were collected to explain the number of wins a major league baseball team has based on the
earned run average (ERA) of the team's starting pitchers
Complete the Table Below
Regression
Statistics
Multiple R
R Square
Adjusted R Square
0.707
Standard Error
Observations
8
ANOVA
Significance F
0.005478716
df
MS
Regression
770.17
Residual
257.83
Total
Standard
Error
Upper
95%
Coefficients
t Stat
P-value
Lower 95%
Intercept
165.46
21.38
0.000
ERA
-21.48
5.07
0.005
Based on the regression results, answer the following questions
a) What is the estimated regression equation?
Y = I65,46 +(-21,48)e,
wins = 165,46 21.48(ERA)
b) What percentage of the variation in wins is explained by ERA?
R2=SSreg SSptal
170,17+257,83 = 1029→770. ni28 50,749 xl 00%
E8 'LSZ
There fore
770.17
7492% of the varation in wins exp byt
c) What is the correlation between wins and ERA?
$5trong pos.tive relate btwn wins
anderA Q
Coef - measure of Strength & diretion
r=R -Square =0:14 9 192607 ñ6,gc
d) What is the standard error of the error term in the regression equation?
SE = SSResidual
n -2 =257.838-242,97166667 56.56
e) Is the coefficient on the variable “ERA" statistically significantly different than 0 at the 10% level
of significance? How do you know?
The Independent variable ERA is Signicicant
Reason: the p-value correspond,ng to ERA
is 0,005 which is < the
Sig Tevel
8.
Transcribed Image Text:5) Data were collected to explain the number of wins a major league baseball team has based on the earned run average (ERA) of the team's starting pitchers Complete the Table Below Regression Statistics Multiple R R Square Adjusted R Square 0.707 Standard Error Observations 8 ANOVA Significance F 0.005478716 df MS Regression 770.17 Residual 257.83 Total Standard Error Upper 95% Coefficients t Stat P-value Lower 95% Intercept 165.46 21.38 0.000 ERA -21.48 5.07 0.005 Based on the regression results, answer the following questions a) What is the estimated regression equation? Y = I65,46 +(-21,48)e, wins = 165,46 21.48(ERA) b) What percentage of the variation in wins is explained by ERA? R2=SSreg SSptal 170,17+257,83 = 1029→770. ni28 50,749 xl 00% E8 'LSZ There fore 770.17 7492% of the varation in wins exp byt c) What is the correlation between wins and ERA? $5trong pos.tive relate btwn wins anderA Q Coef - measure of Strength & diretion r=R -Square =0:14 9 192607 ñ6,gc d) What is the standard error of the error term in the regression equation? SE = SSResidual n -2 =257.838-242,97166667 56.56 e) Is the coefficient on the variable “ERA" statistically significantly different than 0 at the 10% level of significance? How do you know? The Independent variable ERA is Signicicant Reason: the p-value correspond,ng to ERA is 0,005 which is < the Sig Tevel 8.
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