Question

Company X is trying to estimate future inspection fees based on prior experience. You (the accountant) requested and gathered from various managers the number of orders received each week,
the average weight of each order, and the average cost of each order. You then compared this data to the actual inspection fees incurred. The data is summarized below:
Week	Inspection Fees	# orders received	Size of order (lbs)	Cost of order
Week 1	$57,600	219,379	889,114	$25,847
Week 2	$36,500	126,965	320,181	$12,748
Week 3	$40,500	197,583	700,000	$43,910
Week 4	$47,200	231,072	539,044	$9,421
Week 5	$54,700	255,388	677,425	$20,382
Week 6	$56,500	142,072	396,396	$16,329
Week 7	$39,500	151,618	468,812	$11,097
Week 8	$30,400	90,306	267,177	$10,190
Week 9	$20,000	72,718	187,030	$6,082
Week 10	$50,000	123,008	466,636	$16,723
Week 11	$30,000	126,341	135,045	$2,932
Week 12	$20,000	41,988	204,808	$4,202
Week 13	$42,900	155,783	576,713	$9,420
Week 14	$55,300	266,358	603,139	$19,635
Week 15	$28,000	46,367	211,147	$9,319
Total	$609,100	2,246,946	6,642,667	$218,237
Per Week	40607	149796	442844	$14,549

Regression

You take your estimate for Week 16 to the boss and he/she seemed skeptical of the results. The boss sends you back to do some more work. You decide to use regression.

Run regression analysis for the two most promising variables. Compare the coefficient of determination for each.

Which one has the highest coefficient of determination? Construct a cost equation.

Independent variable with the highest coefficient of determination is:

New Cost equation is: Using your new cost equation developed above, redo your estimate for week 16 inspection fees. Compare your results to your earlier answer using the high-low method. New estimate for week 16 using new cost equation: Compare results to earlier prediction using high/low method:

Answer 1

Hello,

1) Fit the regression equation on the # order recived and size of order,

Regression Statistics
Multiple R	0.84771874
R Square	0.718627062
Adjusted R Square	0.671731572
Standard Error	7400.670927
Observations	15
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	17210.17982	4642.097689	3.707414	0.002995	7095.918	27324.44	7095.918	27324.44
# orders received	0.087803737	0.049044137	1.7903	0.098648	-0.01905	0.194662	-0.01905	0.194662
Size of order (lbs)	0.02313183	0.015825279	1.461701	0.169511	-0.01135	0.057612	-0.01135	0.057612

2) Fit the regression equation on the # order recived and Cost of order

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.82227
R Square	0.676129
Adjusted R Square	0.62215
Standard Error	7939.92
Observations	15
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	18227.57	4921.79	3.703445	0.003017	7503.916	28951.23	7503.916	28951.23
# orders received	0.136624	0.035557	3.842413	0.002342	0.059152	0.214096	0.059152	0.214096
Cost of order	0.131505	0.247827	0.530634	0.605354	-0.40846	0.671473	-0.40846	0.671473

3) Fit the regression equation on the # order recived and Cost of order

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.809003
R Square	0.654486
Adjusted R Square	0.596901
Standard Error	8200.92
Observations	15
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	19843.18	4854.57	4.087525	0.001506	9265.977	30420.38	9265.977	30420.38
Size of order (lbs)	0.05336	0.01475	3.617689	0.003529	0.021223	0.085497	0.021223	0.085497
Cost of order	-0.19705	0.318601	-0.61847	0.547826	-0.89122	0.497128	-0.89122	0.497128

from amumg the above 3 regression output the 1)  # order recived and size of order has higest coefficiant of determination.

so most promising regression equation ,

Inspection Fees = 17210.18 + 0.088  # order recived + 0.023 *  size of order ............ regression equation

Q) Which one has the highest coefficient of determination? Construct a cost equation.

regression results for the

1) # orders received

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.817636412
R Square	0.668529302
Adjusted R Square	0.643031556
Standard Error	7717.407793
Observations	15
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	18569.93198	4742.578	3.915578	0.001773	8324.215	28815.65	8324.215	28815.65
# orders received	0.147111244	0.02873	5.120464	0.000197	0.085044	0.209179	0.085044	0.209179

2) Size of order

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.802167642
R Square	0.643472925
Adjusted R Square	0.616047765
Standard Error	8003.779875
Observations	15
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	19982.98048	4732.733	4.222292	0.000997	9758.532	30207.43	9758.532	30207.43
Size of order (lbs)	0.046570947	0.009614	4.843849	0.000321	0.0258	0.067342	0.0258	0.067342

3) cost of order

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.52693
R Square	0.277655
Adjusted R Square	0.22209
Standard Error	11392.55
Observations	15
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	30992.75	5210.515	5.948116	4.84E-05	19736.11	42249.38	19736.11	42249.38
Cost of order	0.66079	0.295604	2.235386	0.043566	0.022175	1.299405	0.022175	1.299405

we fit the three variable sapratly and calculated coefficiant of determination.

# orders received has higest R-square value

Independent variable with the highest coefficient of determination is: # orders received