Question from chapter 5 1
Chapter5: Question 4 under `Demand Estimation.`
4)Startwith four columns: "x","(xM_{x})^{2"},"y", "(yM_{y})^{2"}

Input the data for group X in column x, and similarly for group Y in column y

Compute mean for the two groups

Compute deviation scores for the groups by subtracting each score from its group mean, square it and put these in the columns "(xM_{x})^{2}" and "(yM_{y})^{2"}

Sum the squared deviation scores for individual groups

Calculate S^{2} for each of the groups

Initiate the formula

Compute t

Confirm to establish whether t is statistically significant on the probability table with df = N2 and p < .05 (N = total number of scores)
Formula
M = mean n = number of scores per group 

x = individual scoresM = meann= number of scores in group 
Thebasis for using the rule is that absolute value of t is greater than2.The estimated coefficient is also significant at the 5% level(Davisand Pecar, 2013). Without the basis, it cannot be utilized. It isadvised to check the assumption before starting computation.
Questionsfour and eight under `Forecasting.`
CHAPTER5 Questions 4
4)a) When a company experiences a rise in the number of orders forgoods, It indicates that its production of customers’ items willincrease in the future. If new requests are fewer than in the past,then there will be a drop in the consumer goods to be produced in thefuture. The reverse is also true. When a business experiences adecline in the number of products ordered, then the production ofconsumer goods will fall in the future
Whena business experiences a rise in orders for nondefense capital goods,it indicates that the firms will produce more capital goods in thetimes to come. When there are fewer orders of products of this kind,the production of capital goods will be lower in future.
b)The index of industrial production is an appropriate coincidentindicator because changes in the level of this indicator usually showsimilar changes in overall economic activity, and therefore grossdomestic product (GDP). The index show changes onmonthtomonth and yearoveryear levels. It thus indicatesshortterm ratesof change and business cycle growth, respectively.
c)The Federal Reserve places this interest rate to respond to economicgrowth rates. It is also to stimulate growth. It will be set low fora period after the economy is recovering. Many banks use the primerate to price loan products like student loans and credit card.
8)Exponential smoothing smoothens data. It helps in studies of airturbulence where you would expect significant spikes in data.
Movingaverage is frequently employed to timeseries data to smooth out shortterm fluctuations andemphasize longerterm trends or cycles. The threshold between shortand longterm depends on the application, and the parameters of themoving average set accordingly. For example, in technicalanalysis of financial information like stock prices.
Bothtechniques apply when random fluctuations occur as opposed tocyclical and seasonal variations. It is also advisable to use the twowhen the direction of the series changes infrequently, and the serieslacks a strong trend.
Themoving average method is more useful than exponential smoothingbecause it emphasized longterm trends. It provides greaterflexibility by providing more control on the weighting.
Problem2 under `Demand Estimation.`
Month 
Price 
Quantity 
Jan 
12500 
15 
Feb 
12200 
17 
March 
11900 
16 
April 
12000 
18 
May 
11800 
20 
June 
12500 
18 
July 
11700 
22 
August 
12100 
15 
Sept 
11400 
22 
Oct 
11400 
25 
Nov 
11200 
24 
Dec 
11000 
30 
Jan 
10800 
25 
Feb 
10000 
28 
a)Discounts will result in an increase in quantity sold and henceshould be adopted. As the price goes down, the quantity demanded ofthe commodity increases.
b)Other factors in the regression analysis are income and revenue.
Itmay be difficult to plot the other elements due to full utilizationof the axes by current factors, and also there will be a need tocollect additional data to establish how they impact price andquantity. Customers may also be unwilling to disclose personalinformation like their income for the study.
Problems8 and ten under `Forecasting`.
St=43.6+0.8t 

Month 
Index 
t for 2013 Months 
St=43.6+0.8t 
Forecast 2013 =St*Index 

Jan 
60 
61 
92.4 
5544 

Feb 
70 
62 
93.2 
6524 

March 
85 
63 
94 
7990 

April 
110 
64 
94.8 
10428 

May 
110 
65 
95.6 
10516 

June 
100 
66 
96.4 
9640 

July 
90 
67 
97.2 
8748 

August 
80 
68 
98 
7840 

September 
95 
69 
98.8 
9386 

Oct 
110 
70 
99.6 
10956 

Nov 
140 
71 
100.4 
14056 

Dec 
150 
72 
101.2 
15180 
t=sumof months from Jan 2008 to 2013 with Jan 2013 being month 61, Feb2013 being month 62. The fourth column, title forecast, shows theforecasted monthly sales for the year 2013.
Thet= is replaced in the formulae St= 43.6+0.8t to get the monthlysales. St is then multiplied by the index to arrive at the salesforecast for 2013
Problem10 under forecasting
Problem 10 forecasting 

Growth rate 
0.015 

Intercept 
1376 

Forecasted Temp 
17.1 

Prior day Temp 
3.7 

Forecasted wind speeds 
4.2 

Q=(1+G)*(a+b_{1}T+b_{2}P+b_{3}W) 

Substituting in the equation 

Q=(1+0.015)*(137617.1*40+3.7*37+4.2*8) 

597.5305 
Thecompany demand forecast equation is Q= (1+G)*(a+b_{1}T+b_{2}P+b_{3}W).With the coefficients provided, we substitute. This enables us to getthe future demand. We are thus able to predict gas demand for thatday.
ModelF
Thismodel has two cross price independent variables. Both arestatistically significant and act as a substitute and a compliment toZinfandel. Merlot’s variable becomes significant at a level of 10%.Model F is thus the best specification. Its adjusted R^{2 }isthe highest, and its standard of the estimate is the lowest when wecompare to the rest of the regression on the table (Keat,Young and Erfle, 2013).Merlot compliments while Chardonnay substitutes white zinfandel inthe specification.
ModelG
Ithas two independent variables that are the cross price. Onesubstitute while the other compliments white zinfandel (Keat,Youngand Erfle, 2013). They are both statistically insignificant. It isevident in the attached workbook.
ModelH
Apartfrom having the price of white zinfandel, this model also includesthree cross prices. The additional file attached provides thisanalysis. It is possible to see how this H model compares to therest. We also see its shortfall when it comes to statisticalsignificance.
ExcelInterpretation
Kindlynote that the count that I was able to use was only 17 since thosewere the only visible observations from your jpeg pictures. Kindlyimpute the other rows (19 to 52) and include them in the formula forregression to obtain the exact duplication of your data. This linkwill show you how to manipulate the data to achieve this. http://www.exceleasy.com/examples/regression.html
RSquare 0.98. This fit is good. 96% of the variations in the quantitysold is due to variables InQWZ, InPWZ, InPCH, InPCS, InPM, time, andPeak.
Pand FValues.
Tosee if our results are reliably significant when it comes tostatistics, we look at the F significance value=3.3900.
Weproceed to delete the variable whose p values that exceed 0.5 untilthe significance falls below 0.5.
Thecoefficients are used to derive an equation for forecasting.
Theresiduals tell us how far our data is from the predicted points ofdata. These residuals can be used to create a scatter plot
Reference
Keat,P.G., Young, P.K.Y. & Erfle, S.E. (2013). Managerial Economics(7th edition).UpperSaddle River, NJ: Pearson Prentice Hall.