Question

Dean made a statistical estimation of the cost-output relationship for a shoe store. The data for the firm is given in the following table. x 4.5 7 9 10 15 20 33 50 y 3 3.3 3.4 3.5 4.5 5.5 7.5 12 Here x is the output in thousands of pairs of shoes, and y is the cost in thousands of dollars. A. Determine the best-fitting line (using least squares). S1(x) = Incorrect: Your answer is incorrect. r2 = B. Determine the best-fitting quadratic (using the least squares) and the square of the correlation coefficient. S2(x) =

Answer 1

Dean made a statistical estimation of the cost-output relationship for a shoe store. The data for the firm is given in the following table.

x 4.5 7 9 10 15 20 33 50

y 3 3.3 3.4 3.5 4.5 5.5 7.5 12

Here x is the output in thousands of pairs of shoes, and y is the cost in thousands of dollars.

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis.

1. Determine the best-fitting line (using least squares).

y = 1.701+0.196*x

S1(x) = standard error = 0.4055

r2 = 0.9852

Regression Analysis
	r²	0.9852	n	8
	r	0.9926	k	1
	Std. Error of Estimate	0.4055	Dep. Var.	y
Regression output						confidence interval
variables		coefficients	std. error	t (df=6)	p-value	95% lower	95% upper
Intercept	a =	1.701
x	b =	0.196	0.010	19.966	1.02E-06	0.172	0.220
ANOVA table
Source	SS	df	MS	F	p-value
Regression	65.552	1	65.552	398.65	1.02E-06
Residual	0.987	6	0.164
Total	66.539	7

2. Determine the best-fitting quadratic (using the least squares) and the square of the correlation coefficient.

Y=2.460+0.103*x+0.002*x²

S2(x) =0.2015

R square = 0.9969

Regression Analysis
	R²	0.9969
	Adjusted R²	0.9957	n	8
	R	0.9985	k	2
	Std. Error of Estimate	0.2015	Dep. Var.	y
Regression output						confidence interval
variables		coefficients	std. error	t (df=5)	p-value	95% lower	95% upper
Intercept	a =	2.460
x	b1 =	0.103	0.022	4.736	.0052	0.047	0.159
xx	b2 =	0.002	0.0003947	4.394	.0071	0.001	0.003
ANOVA table
Source	SS	df	MS	F	p-value
Regression	66.336	2	33.168	817.03	5.14E-07
Residual	0.203	5	0.041
Total	66.539	7