Question

1. Odie Company manufactures a popular brand of cat repellant known as Cat-B-Gone, which it sells in gallon-size bottles with a spray attachment. The majority of Odie's business comes from orders placed by homeowners who are trying to keep neighborhood cats out of their yards. Odie's operating information for the first six months of the year follows:

Required:

1. Prepare scattergraph of Odie's operating cost and draw the line you believe best fits the data.
2. Based on this graph, estimate Odie's total fixed costs per month.
3. Using the high-low method, calculate Odie's total fixed operating costs and variable operating cost per bottle.
4. Perform a least-squares regression analysis on Odie's data.
5. Determine how well this regression analysis explains the data.
6. Using the regression output, create linear equation (y = a + bx) for estimating Odie's operating costs.

Sigrid's Custom Graphics specializes in creating and painting store window advertisement displays. The majority of its business comes from local retailers and fast-food restaurants.

A portion of Sigrid's operating information for the past year follows:

1. Prepare scattergraph of Sigrid's operating cost and draw the line you believe best fits the data.
2. Based on this graph, estimate Sigrid's total fixed costs per month.
3. Using the high-low method, calculate Sigrid's total fixed operating costs and variable operating cost per window.
4. Using the high-low method results, calculate the expected operating cost for the business if it paints 96 windows.
5. Perform a least-squares regression analysis on Sigrid's data.
6. Using the regression output, create linear equation (y = a + bx) for estimating Sigrid's operating costs.
7. Using the least-squares regression results, calculate the store's expected operating cost if it paints 96 windows.

Month Number of Bottles Sold Operating Cost 8,000 January February 1,000 1.100 7,700 March 1,300 2,000 9,900 14,000 April May 2,400 17,250 June 3,000 20,000 Number of Window Displays Month Operating Cost $1,540 January February 40 42 1,720 66 March 2.100 April May 75 2,675 80 3,250 3,760 June 83 July August September 81 3,270 88 3,220 80 2,980 2,090 October 58 November 67 1,950 December 77 2,925

Answer 1

		X	Y	1399+6.34*X
	Month	Number of Bottles Sold	Operating Cost	Projected Operation Cost
	January	1,000	$8,000	$7,739
	February	1,100	$7,700	$8,373
	March	1,300	$9,900	$9,641
	April	2,000	$14,000	$14,079
	May	2,400	$17,250	$16,615
	June	3,000	$20,000	$20,419
	HIGH AND LOWMETHOD:
	Y =a +bX
	LOW: X1=1000, Y1=8000
	HIGH: X2=3000, Y2=20000
	8000=a+b*1000………Equation(1)
	20000=a+b*3000…… Equation (2)
	Multiplying Equation (1) by 3
	24000=3a+b*3000……….Equation(3)
	Subtracting Equation (2) from equation(3)
	4000=2a
	a=4000/2=2000
	8000=a+b*1000………Equation(1)
	8000=2000+b*1000
	b=6000/1000=6
	LEAST SQUARE REGRESSION ANALYSIS
	Click on Data
	Click on Analysis
	Select Regression and click"Ok"
	Input Y range
	Input X range
	ClickOk
	Output is given below
	SUMMARY OUTPUT
	Regression Statistics
	Multiple R	0.995496641
	R Square	0.991013563
	Adjusted R Square	0.988766954
	Standard Error	541.5505928
	Observations	6
	ANOVA
		df	SS	MS	F	Significance F
	Regression	1	129368975	129368975.2	441.1152	3.04E-05
	Residual	4	1173108.2	293277.0445
	Total	5	130542083
		Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
	Intercept	1399.016563	586.4965	2.385379205	0.075546	-229.359	3027.392	-229.359	3027.392
	X Variable 1	6.338509317	0.3017943	21.00274373	3.04E-05	5.500594	7.176425	5.500594	7.176425
	a=Intercept	1399.0165631
	b= X variable 1	6.338509317
	Y=1399+6.34X
	R square=0.991013563
	This means 99% data are explained by this equation
	Operating Cost(Scattergraph) $25,000 $20,000 $15,000 Operating Cost(Scattergraph) $10,000 $5,000 $0 1,000 2,000 2,500 3,000 500 1,500 3,500 Operating Cost(Line) $25,000 $20,000 $15,000 -Operating Cost(Line) $10,000 $5,000 500 1,000 1,500 2,000 2,500 3,000 3,500