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.

	Sales				Earnings						Sales				Earnings
Company	($ millions)				($ millions)				Company		($ millions)				($ millions)
Papa John’s International	$	91.1				5.2				Checkmate Electronics	$	17.7				2.6
Applied Innovation		20.3				4.6				Royal Grip		13.1				1.7
Integracare		18.3				1.4				M-Wave		21.4				3.8
Wall Data		72.0				8.5				Serving-N-Slide		55.5				8.2
Davidson & Associates		62.5				6.9				Daig		30.6				6.2
Chico’s FAS		49.8				4.4				Cobra Golf		75.3				13.1

1. Draw a scatter diagram.

Let sales be the independent variable and earnings be the dependent variable. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

b.	The coefficient of correlation is
c.	The regression equation, with the coefficients, is ŷ =		+		x
d.	For a small company with $50 million in sales, an estimate of the earnings is		($ millions).

Answer 1

a)

b)

b)

correlation r='Sxy/(√Sxx*Syy) =

0.717

c)

regression equation : y^ =1.684+0.088x

d)

predicted val=1.684+50*0.088=

6.0840

(please try 6.081 million if this comes wrong)