A recent article in Bloomberg Businessweek listed the “Best Small Companies.” We

Question

A recent article in Bloomberg 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. (Round your answers to 3 decimal places.)

For a small company with $46 million in sales, an estimate of the earnings is  ($ millions).

A recent article in Bloomberg 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.

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Earnings
Independent Variable: Sales
Earnings = 1.8807069 + 0.0821918 Sales
Sample size: 12
R (correlation coefficient) = 0.66490932
R-sq = 0.4421044
Estimate of error standard deviation: 2.5440323

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

a) Coefficient of correlation = 0.665

b) Coefficient of determination = 0.442

c) Regression equation:

y = 1.88 + 0.08 x

d) For x = 46,

y = 5.662

Hence,

For a small company with $46 million in sales, an estimate of the earnings is $ 5.662 millions.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 1.8807069 1.4320919 0 10 1.3132586 0.2184 Slope 0.0821918 0.02919729 0 10 2.8150489 0.0183

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