Question

Is it possible to predict the annual number of business bankruptcies by the number of firm births (business starts)? The following table shows the number of business bankruptcies (1,000s) and the number of firm births (10,000s) for a six-year period. Use these data to develop the equation of the regression model to predict the number of business bankruptcies by the number of firm births. Discuss the meaning of the slope.

Business Bankruptcies (1,000s)	Firm Births (10,000s)
34.8	58.1
35.0	55.8
38.5	57.0
39.8	58.5
35.5	57.4
37.9	58.0

r =

The r value represents a relatively :

strong positive, strong negative , moderate positive or moderate negative. (choose one)

relationship between the number of firm births and the number of business bankruptcies.

Y is ________________ + X is _______________________

The slope of the line means that for every 10,000 increase of firm births, the number of business bankruptcies is predicted to increase by ______________

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Answer 1

We want to know if bankrutcies can be predicted by number of births .So our independent variable is birth (x) and bankruptcies is 'y'.

	Business Bankruptcies	Firm Births
	(1,000s) (y)	(10,000s) (x)	y^2	x ^2	xy
1	34.8	58.1	1211.04	3375.61	2021.88
2	35	55.8	1225	3113.64	1953
3	38.5	57	1482.25	3249	2194.5
4	39.8	58.5	1584.04	3422.25	2328.3
5	35.5	57.4	1260.25	3294.76	2037.7
6	37.9	58	1436.41	3364	2198.2
Total	221.5	344.8	8198.99	19819.26	12733.58

Correlation coefficient

Since this 0 < r <0.5, it is positive and not very strong.

The r value represents a relatively :

strong positive, strong negative , moderate positive or moderate negative.

The regression eqaution is given by

slope =

= 0.9916

   intercept

= -20.066

Theefore the equation is

Here 'y' represents per 1000 bankruptcies where 'x' represents per 10000. For 10000 increase in births mean a unit increase in 'x' there will be 0.9916 units increase in 'y'. This will be multiplied by 1000 to get increase in bankruptcies

= 0.9916 * 1000 = 991.6

The slope of the line means that for every 10,000 increase of firm births, the number of business bankruptcies is predicted to increase by 992.

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