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Problem!5 The following shows the productivity (P) of a transfer line, it is function of the size of the amortization storage (2) and the repair ratio of the production machines (p) 50 60 65 70 75 80 9.0 2 8.0 7.0 6.0 6.0 5.0 5.1 4 9 15 20 38 60 85 140 85 90 93 95 4.8 4.4 10 4.3 a) Which model appears to be the most appropriate? b) Estimate the parameters of the suggested model. C) How much will the productivity be if 2s 180 and -3.57

Answer 1

(a) Multiple linear regression:

Regression Analysis
	R²	0.979
	Adjusted R²	0.972	n	10
	R	0.989	k	2
	Std. Error	2.497	Dep. Var.	P
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,988.4641	2	994.2321	159.49	1.45E-06
Residual	43.6359	7	6.2337
Total	2,032.1000	9
Regression output					confidence interval
variables	coefficients	std. error	t (df=7)	p-value	95% lower	95% upper	std. coeff.
Intercept	118.3723						0.000
Z	0.0812	0.0267	3.042	.0188	0.0181	0.1443	0.242
p	-7.5795	0.7535	-10.059	2.06E-05	-9.3613	-5.7978	-0.801
Predicted values for: P
			95% Confidence Interval		95% Prediction Interval
Z	p	Predicted	lower	upper	lower	upper	Leverage
180	3.5	106.460	99.644	113.276	97.443	115.477	1.333

A linear model seems appropriate

(b) b0 = 118.3723, b1 = 0.0812, p = -7.5795

The regression equation is P = 118.3723 + 0.0812 Z - 7.5795p

(c) Predicted P = 106.46