The following table gives the 2015 total payroll (in millions of dollars) and th

Question

The following table gives the 2015 total payroll (in millions of dollars) and the percentage of games won during the 2015 season by each of the National League baseball teams. Arizona Diamondbacks Atlanta Braves Chicago Cubs Cincinnati Reds Colorado Rockies Los Angeles Dodgers Miami Marlins Milwaukee Brewers New York Mets Philadelphia Phillies Pittsburgh Pirates San Diego Padres San Francisco Giants St. Louis Cardinals 41 119 102 57 42 105 101 136 101 173 121 165 (a) Find the least squares regression line with total payroll as the independent variable and percentage of games won as the dependent variable (b) Is the equation of the regression line obtained in part a the population regression line? Why or why not? Do the values of the y-intercept and the slope of the regression line give A and B or a and b? (c) Give a brief int of the values of the y-intercept and the slope obtained in part a (d) Predict the percentage of games won by a team with a total payroll of $150 million .il 3(12pt) :) T.E. E .,0. T T T (Arial

Explanation / Answer

using excel

y^ = 44.0083 + 0.0440 * x

b) this is not population regression line , it is sample regression line

c) b^ gives the change in y , when x is changed by 1 unit

a^ is the value of Y when X is 0

d)

when x = 150

y^ = 44.0083 + 0.0440 * 150

= 50.6083

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SUMMARY OUTPUT Regression Statistics Multiple R 0.267891437 R Square 0.071765822 Adjusted R Square 0.000363193 Standard Error 8.165232077 Observations 15 ANOVA df SS MS F Significance F Regression 1 67.01013997 67.01013997 1.005086545 0.334379343 Residual 13 866.7231934 66.67101487 Total 14 933.7333333 Coefficients Standard Error t Stat P-value Lower 95% Intercept 44.00825591 5.838510038 7.537583327 4.26488E-06 31.39492183 x 0.044043121 0.043931533 1.002540046 0.334379343 -0.050865185

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