Question

A production plant cost-control engineer is responsible for cost reduction. One of the costly items in his plant is the amount of water used by the production facilities each month. He decided to investigate water usage by collecting seventeen observations on his plant's water usage and other variables.

Variable               Description

Temperature     Average monthly temperate (F)

Production          Amount of production (M pounds)

Days                      Number of plant operating days in the month

Persons                Number of persons on the monthly plant payroll

Water                   Monthly water usage (gallons)

Temperature	Production	Days	Persons	Water
58.8	7107	21	129	3067
65.2	6373	22	141	2828
70.9	6796	22	153	2891
77.4	9208	20	166	2994
79.3	14792	25	193	3082
81.0	14564	23	189	3898
71.9	11964	20	175	3502
63.9	13526	23	186	3060
54.5	12656	20	190	3211
39.5	14119	20	187	3286
44.5	16691	22	195	3542
43.6	14571	19	206	3125
56.0	13619	22	198	3022
64.7	14575	22	192	2922
73.0	14556	21	191	3950
78.9	18573	21	200	4488
79.4	15618	22	200	3295

i. Create the Scatter Plot graph between “water” and “production”

ii. Use the appropriate routine of Data Analysis in MS Excel or any other statistical software in order to estimate the correlation matrix of all variables

iii. Compute 95% confidence interval for the values of the correlation coefficient between and determine which ones are statistically significant”

Answer 1

i. Create the Scatter Plot graph between “water” and “production”

ii. Use the appropriate routine of Data Analysis in MS Excel or any other statistical software in order to estimate the correlation matrix of all variables

	Temperature	Production	Days	Persons	Water
Temperature	1.000
Production	-.024	1.000
Days	.438	.106	1.000
Persons	-.082	.918	.032	1.000
Water	.286	.631	-.089	.413	1.000
	17	sample size
	± .482	critical value of r .05 (two-tail)
	± .606	critical value of r .01 (two-tail)

iii. Compute 95% confidence interval for the values of the correlation coefficient between and determine which ones are statistically significant”

The significant correlations are:

(i) Persons & Production

(ii) Water & Production