Question

24. United Widget Manufacturing has a problem with defective widgets. Employees make hundreds of thousands of them each day, and many are defective. United has instituted training for the workers, and you would like to predict the number of defects per week based on the number of days of training an employee has received. You obtain the following data: ST Employee number 1015 2023 1153 4029 1117 0012 Days of training 4 5 6 4 3 2 Defects per week (100's) 19 17 7 14 22 23 (a) Determine the regression equation Answer: (b) Interpret the meaning of the slope using the words of the problem.

Answer 1

Question 24:

(a) y = 31.8 - 3.7*x

(b) For every day of training, defects per week will decrease by 3.7.

(c) y = 31.8 - 3.7*6 = 9.6

(d) r2 = 0.786782

78.6782% of the variation in the model is explained.

Period	Demand (y)	Period(x)		Forecast	Error	Absolute	Squared	Abs Pct Err
Period 1	19	4		17	2	2	4	10.53%
Period 2	17	5		13.3	3.7	3.7	13.69	21.76%
Period 3	7	6		9.6	-2.6	2.6	6.76	37.14%
Period 4	14	4		17	-3	3	9	21.43%
Period 5	22	3		20.7	1.3	1.3	1.69	05.91%
Period 6	23	2		24.4	-1.4	1.4	1.96	06.09%
				Total	3.55E-15	14	37.1	102.86%
Intercept	31.8			Average	5.92E-16	2.333333	6.183333	17.14%
Slope	-3.7				Bias	MAD	MSE	MAPE
						SE	3.045488
Forecast	9.6	6
						Correlation	-0.88701
						Coefficient of determination	0.786782