Help with my math hw! Please show work and answer all parts of the questions. :)

Question

Help with my math hw! Please show work and answer all parts of the questions. :) Thanks!

Week Sales
26 15200
27 15600
28 16400
29 15600
30 14200
31 14400
32 16400
33 15200
34 14400
35 13800
36 15000
37 14100
38 14400
39 14000
40 15600
41 15000
42 14400
43 17800
44 15000
45 15200
46 15800
47 18600
48 15400
49 15500
50 16800
51 18700
52 21400
53 20900
54 18800
55 22400
56 19400
57 20000
58 18100
59 18000
60 19600
61 19000
62 19200
63 18000
64 17600
65 17200
66 19800
67 19600
68 19600
69 20000
70 20800
71 22800
72 23000
73 20800
74 25000
75 30600
76 24000
77 21200

1. Generate supporting Excel spreadsheet(s) and graphs (use scatter plots) to answer the following questions for the Dry Goods 2002-2003 data.

2. Modeling the data linearly - a. Generate a least squares linear regression model for this data.

b. How good is this regression model?

c. What are the marginal sales for this department using the linear regression model?

3. Modeling the data quadratically -

a. Generate a quadratic model for this data.

b. What are the marginal sales for this department using this model?

c. Calculate the model generated relative max/min value. Show backup analytical work.

d. Compare actual and model generated relative max/min value.

4. Comparing models

a. Which model do you feel best predicts future trends? Explain your rationale.

b. Based on the model selected, what type of seasonal adjustments, if any, would be required to meet customer needs?

Explanation / Answer

It is clear that no line can be found to pass through all points of the plot. Thus no functional relation exists between the two variables week(w) and Sales(s). However, the scatter plot does give an indication that a straight line may exist such that some of the points on the plot are scattered randomly around this line. The regression model here is called a simple linear regression model because there is just one independent variable.

The marginal revenue function is the first derivative of the total revenue function. so

S=8741.97+180.99w

TR=(8741.97+180.99w)w

MR=8741.97+361.999w

SUMMARY OUTPUT Regression Statistics Multiple R 0.806575 R Square 0.650563 Adjusted R Square 0.643574 Standard Error 2030.33 Observations 52 ANOVA df SS MS F Significance F Regression 1 3.84E+08 3.84E+08 93.08734 5.29E-13 Residual 50 2.06E+08 4122241 Total 51 5.9E+08 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 8741.975 1006.33 8.686988 1.47E-11 6720.702 10763.25 X Variable 1 180.9997 18.75999 9.648178 5.29E-13 143.3192 218.6803

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