A recent article in BusinessWeek listed the \"Best Small Companies.\" We are int
ID: 3262149 • Letter: A
Question
A recent article in BusinessWeek listed the "Best Small Companies." We are interested in the current results of the companies sales and earnings. A random sample of 12 companies was selected and the sales and earnings, in millions of dollars, are reported below. Let sales be the independent variable and earnings be the dependent variable. (a) Compute the correlation coefficient. (Round your answer to 3 decimal places.) (b) Compute the coefficient of determination. (Round your answer to 3 decimal places.) (c) Determine the regression equation. (Round your answers to 4 decimal places.) (d) For a small company with $60 million in sales, estimate the earnings. (Round your answer to 4 decimal places.)Explanation / Answer
Regression output form Excel:
Sola:
corrrelation coeff=multipler from output=0.692
Solutionb:
coefficient of determination =r sq=0.479
Solutionc:
regression eq is
y=1.8671+0.0835x
Solutiond:
x=60
y hat=1.8671+0.0835(60)
=6.8771
Estiamted earnings=6.8771 millions
SUMMARY OUTPUT Regression Statistics Multiple R 0.691764 R Square 0.478537 Adjusted R Square 0.426391 Standard Error 2.375959 Observations 12 ANOVA df SS MS F Significance F Regression 1 51.80487 51.80487 9.176834 0.012692 Residual 10 56.45179 5.645179 Total 11 108.2567 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1.86714 1.348219 1.384894 0.196201 -1.13688 4.87116 -1.13688 4.87116 sales 0.083503 0.027565 3.029329 0.012692 0.022085 0.144922 0.022085 0.144922