Quantitative Methods for Business

Homework6.xlsx

Prob 1

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
1. (5 pts) A company has profit ($000) and revenue ($000) over the past 9 periods.
	Revenue	Profit
	19	1
	20	1
	32	3
	33	4.5
	35	2
	45	6
	70	8
	70	10
	100	11
	a. Calculate the Spearman rank correlation coefficient between revenue and profit
	b. Calculate the Pearson product moment correlation coefficient for revenue and profit
	c. Comment on the association between revenue and profit.

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
2. (5 pts) A study was conducted to determine the relationship between travel miles and charges on the
American Express card. A research firm selected a random sample of 25 cardholders and recorded
total miles traveled and total credit charges over a specified period.
Miles	Dollars
1211	1802	a. Construct a scatterplot of miles (x) versus dollars (y)
1345	2405
1422	2005
1687	2511	b. Determine the linear regression equation for travel expense dollars based
1849	2332	on miles driven. Be sure to write your answer in equation form.
2026	2305	[Hint: try the "Add Trendline" function as described in the practice exercises.]
2133	3016
2253	3385
2400	3090
2468	3694
2699	3371
2806	3998
3082	3555	c. Plot the regression line on your scatterplot
3209	4692
3466	4244
3643	5298
3852	4801
4033	5147
4267	5738
4498	6420
4533	6059
4804	6426
5090	6321
5233	7026
5439	6964

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
3. (5 pts) You are a naturalist capturing wild black bears to measure their approximate age (in months) and weight (in kilograms).
AGE	WEIGHT
19	80	a. Determine the linear regression equation for age (x) and weight (y).
55	344
81	416
115	348
104	166
100	220
56	262	b. Calculate the coefficient of determination, r2.
51	360
57	204
53	144
68	332	c. You are preparing a symposiom presentation of your findings and wish to make a key
8	34	point of the coefficient of determination. How would you interpret or explain your
44	140	calculated r2 value?
32	180
20	105
32	166
45	204
9	26
21	120
177	436
57	125
81	132
21	90
9	40
45	220
9	46
33	154
57	116
45	182
21	150
10	65
82	356
70	316
10	94
10	86
34	150
34	270
34	202
58	202
58	365
11	79
23	148
70	446
11	62
83	236
35	212
16	60
16	64
17	114
17	76
17	48
8	29
83	514
18	140

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
4. (5 pts) A health insurer estimates the cost of treatment (y) based on the average number of
hospitalization days recommended by the examining physician (x).
		y = 453.96 + 11207.28x
	a. If an examining physician recommends a hospital stay of 6 days, what
	is the estimated treatment cost?
	b. What is the expected increase in treatment cost for every additional
	day of hospitalization?

This is a graded assignment reflecting your own work only. Students are not permitted assistance from other students or tutors.
5. (5 pts) Assume inventory is growing by day. Make a scatterplot of the data and use "Add Trendline" to fit 2 non-linear
trends: Power and Polynomial (order=3). Which one fits the data best and why?
	[Hint: compare coefficients of determination for the 2 models.]
	Day	Inventory
	1	134
	2	267
	3	456
	4	390
	5	777
	6	978
	7	1510
	8	1800
	9	2560
	10	4250

1.b. r = 0.954

2.b. slope = 1.255

2.c.

3.a. Weight = 65.2 + 2.71*Age

4.a. Cost = $67,697.64