Question

	Sales	Earnings
Checkmate Electronics	89.2	4.90
Royal Grip	18.6	4.40
M-Wave	18.2	1.30
Serving-N-Slide	71.7	8.00
Daig	58.6	6.60
Cobra Golf	46.8	4.10
Papa John's International	17.5	2.60
Applied Innovation	11.9	1.70
Integracare	19.6	3.50
Wall Data	51.2	8.20
Davidson & Associates	28.6	6.00
Chico's FAS	69.2	12.80

1. A recent article in a companies business digest listed the “Best Small Companies.” We are interested in the current results of the companies’ sales and earnings. A random sample of the 12 companies was selected and the sales and earnings, in millions of dollars, are reported in the Excel File.

1. The Regression equation for this data set is Ꞌy =
2. Calculate the correlation coefficient
3. What is the estimate of earnings for a company with $40 million in sales
4. What is the IV?
5. What is the DV?
6. What is the Y intercept?
7. What is the slope?
8. What is the estimate of earnings for a company with $10 in sales?

Answer 1

The regression output is attached in the below image

Question (a)

Regression equation is

Earnings = Sales * 0.12848 + 0.57079

Where Earnings and Sales are in $ millions

Question (b)

Correlation coefficient r = d_x dy /  d_x²d_y²

Where d_x dy = xy - (xy) / n

d_x² = x² - (x)² / n

d_y² = y² - (y)² / n

Here x is Sales and y is earnings

x = 501.1

y = 64.1

xy = 3306.35

x² = 28458.99

y² = 458.41

d_x dy = xy - (xy) / n

= 3306.35 - (32120.51) / 12

= 3306.35 - 2676.709

= 629.64

d_x² = x² - (x)² / n

= 28458.99 - (251101.2) / 12

= 28458.99 - 20925.1

= 7533.889

  d_y² = y² - (y)² / n

= 458.41 - (4108.81) / 12

= 458.41 - 342.40

= 116.009

r = d_x dy /  d_x²d_y²

= 629.64 / 7533.889 * 116.009

= 629.64 / 874000.2

= 629.64 / 934.879

= 0.6734

So correlation coefficient = 0.6734

Question (c)

Estimate of earnings for a company with $40 million in sale

Regression equation is Earnings = Sales * 0.12848 + 0.57079

So earnings = 40 * 0.12848 + 0.57079

= 5.13824 + 0.57079

= 5.71002

= 5.71 rounded to 2 decimals

So earnings is $5.71 million

Question (d)

The independent variable is Sales in $ millions

Question (e)

The dependent variable is Earnings in $ millions

Question (f)

The y-intercept is the intercept coefficient value which is 0.57059

Question (g)

The y-intercept is the Sales coefficient value which is 0.12848

Question (h)

Estimate of earnings for a company with $10 in sales

Regression equation is Earnings = Sales * 0.12848 + 0.57079

So earnings = 10 * 0.12848 + 0.57079

= 1.28481 + 0.57079

= 1.85560

= 1.86 rounded to 2 decimals

So earnings is $1.86  million