quantittative techniques in business

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Month Sales Price advert exp no. househol ds av salesexp mean daily january 75 6.8 2 515 10 2.4 febuary 90 6.5 5 542 148 4 march 148 6 6 576 18 5.2 April 183 3.5 7 617 11 6.8 May 242 3 22 683 14 8 June 263 2.9 25 707 18 8.4 July 278 2.6 28 500 17 10.4 august 318 2.1 30 742 14 11.5 septembe r 256 3.1 22 747 12 9.6 october 200 3.6 18 770 13 6.1 november 140 4.2 10 515 18 3.4 december 80 5.2 2 542 14 2 Table of contents 1 Executive summary 2 Introduction 3 Descriptive statistics(Task1) sales and price sales and advert sales and experience Executive summary a well structured and an organized business strategy makes business succecful . in order to compete in markert a good business manager must have enough information and knowledge to constructs its business policies and business . we are about to carry out different kind of analysis on its sunglasses firm in order to see firms past events,current position and

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Page 1: quantittative techniques in business

Month Sales Price advert expno. households

av salesexp mean daily

january 75 6.8 2 515 10 2.4febuary 90 6.5 5 542 148 4march 148 6 6 576 18 5.2April 183 3.5 7 617 11 6.8May 242 3 22 683 14 8June 263 2.9 25 707 18 8.4July 278 2.6 28 500 17 10.4august 318 2.1 30 742 14 11.5september 256 3.1 22 747 12 9.6october 200 3.6 18 770 13 6.1november 140 4.2 10 515 18 3.4

december 80 5.2 2 542 14 2

Table of contents 1 Executive summary 2 Introduction 3 Descriptive statistics(Task1) sales and price sales and advert sales and experience

Executive summary a well structured and an organized business strategy makes business succecful . in order to compete in markert a good business manager must have enough information and knowledge to constructs its business policies and business . we are about to carry out different kind of analysis on its sunglasses firm in order to see firms past events,current position and predicting its future values . by carrying out graphical ananlysis through different diagrams we will have a simple view of sunglasses firms past .what have the firm been doing its sales and expenditures . as there are so many expenses of sunglasses firm so it is very important6 to know which if its all expenses are relevant to business and strength of relationship between variables .in 1964 ,a new York teenager named as Eric Bram just realized price of pizza slice was similier to a subway ride .in 1980 he analysed the same and predicted to

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new york times that subway ride will be increased on the bases of pizza slice’s price. Reporter Clyde Heberman wrote that in new York city ,the subway fare and cost of pizza slice “ have run remarkably parallel for decADES .THE SAME WAY WE ARE GOING TO see what are the factors or variables that are could affect the sunglasses sales through regression anal;ysys . these different kind of analysis will make us to see the firm’s position and will help us to form its future strategies to target our goals . IntroductionThere are so many factors in an organization that determines the firm’s position, but if someone want to see the firm’s performance then mainly sales of the organization presents the true picture. The report I am going to write is about a sunglasses firm. We have been given details of its different kind of expenditures and its sales throughout the year. We will carry out different kind of analysis on sales and other variables to figure out what are the relevant factors affecting the turnover and which areas are not relatively not important. in this report we are going to compare the variables I.e. sales and expenditures or sales and price .we will see how the change in the variables effect sunglasses sales . And its all comparison will be gone through by the graphical presentation according to the nature of variables .further more we will see the changes in the variables effecting on sales with the passage of time on monthly basis whether they are increasing or decreasing with the help of correlation matrix. And finally we will analyze the relationship between independent and dependent variables by regression analysis by doing this we will come to know which factors are directly or indirectly affecting the company’s performance . by working out with diagrammatic presentation of data

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helps us to save the time and see the results very quickly ascfc (curwin and slatter ) has said (senior managers are often more interested in general trends in data, rather than immense detail contained in the raw data .

Task 1Descriptive statistics graphical analysis Graphical analysis is a presentation of data in a very siple and quick way . in order to present large numbers and figures to give an overall view diagrammatic presentation is a best way as it is presents all the data on one platform . with the help of provided date we will analyze the relationship between different vaariables one by one 2.1 sales and price 2.2 sales and advert 2.3 sales and experience

Sales and price

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Diagram above explains the relationship between sales and price .according to economic theory law of demand states that more the price less the demand . in other words there is a direct relationship between the price of a product and sales of that product .if the price of the product is high quanrity of sold units will be less and vice versa . as we can clearly see from the above diagram when the price was 6.8 the sales were 75 in first month . moving forward in the second moth of febuary when price decreased to 6.5 the sales of sunglasses gone up to 90.in the same way the price was decreasing by every month until the august when price came down as low as 2.1 pound per unit and our sales went high 318.this is the highest sale all over the year and lowest price indeed . after the august we can clearly see a gradually increase in a price that directly effects the sales and sales gradually keep coming down at the end of the year when price again go up to 5.2 pound the sales came down to 80.looking at the month of august we can easily

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compare the sales and price of the sunglasses in the starting and the end of the year .for better explanation of the relationship of sales and price im going present the relationship in a different view with the help of law of demand curve. (A)

Demand curve clearly explains that more tbe mrice less the quantity supplied as less the price more the demand .

Relationship between Sales and advertising Marketing communications is a nisation. It can be seen as the exchange of processes to create an over time contextual effect on the relationship between the organisation and its customers (Frankelius, 1997)The purpose with marketing communications is to make the organisation and its products well known for its customers along with keeping the customers conscious about the organisation (Engdahl 2006, Iyer, Sobermann & Villas-Boas 2005).

1 2 3 4 5 6 7 8 9 10 11 12Sales

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Diagram above represents the relationship between sales and advertising .although there are so many factors that effects sales directly but the advertising also a major factor that determines the turnover . well with the help of above diagram we can see there is a direct relationship between sales and advertising . the more you spend on advertising more people will come to know about the product .in the first month there was an advertising expense of 2 pounds and sales figure as 75 ,in the march advert expense has gone up to 6 pounds andsales have also increased upto 148.while looking at the table we can see our maximum sales was in the august amounts as 318 and if we look at the advertising expense in august its high as well upto 30. So more we do the advertisement more the sales . well therr are other factors as well I,e generally thyere is no much sun shine in december so there is no need spend lot og money on adverisemnent as people will still not buy because of the weather condition

Sales and experience

Experienced and trained staff are essential for any organization. Well experienced staff is not directly associated with the sales but there is still a relationship between those . it helps a lot when it comes to satisfy the custmers and introduce the products with specifivations of product .it only helps the sales when an organization is succeed to targets the people to come in the store and rest comes up to staff . the way they approach the custumers as major companies like apple , tesco and asda have very trained staff and they help the cutumers all the possible way . As n essential factor in the process of creating a trust among the customers for an orga

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Sales and experience

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Correlation matrix What is correlation (definistion)a correlation exists between two variables when the values of one variable are somehow associated with the values of other variables(Triola,2012) .Correlation according to lucey(2002),is the gross inter relationship or association between variables

Correlation is now a days is very common used term in news papers and regular life its ofntly used to see how is therelationship between two variables .from the statistics point of view correlation is used to see whether two variables are associated with each other and if then how strong is the relationship , for example weight and hight people with more hight are supposed to be more havier as compared to people with less high) .

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Linear correlation coefficient r measures thye strength of the linear correlation between the paired quantitative x and y values in a sample .the linear correlation coefficient is sometimes refferd to as pearson product moment correlation coefficeniet in honour of Karl pearson (1857-1936),who originally developed it . in this report we are going to see what are the factors that are associated with the sales .for example sales and price or sales and advertising or relationship between sales and mean daily hours . we can see there are some of the variables that are directly affecting the sales quantity but in order to see how strong are these factors affecting we will use statistical correlation . the results we get from correlation is called as coefficient of correlation it ranges from -1 to +1. If the results are more close to -1 ot +1 that means they are more related variables .results in -1 indicates that variables are strong negatively related if there is a decrese in the indepent variable it will cause increase in the dependent variable for example sales and price we reduce the price there will be increase in the sales as we discussed earlier in the diagrammatic presentation of sales and price . so in the same way results in +1 indicates there strong positive relationship between two variables if we increase or decrease one variable it will directly decrease or increase in thye same way . with the help of excel we are going to study correlation analysys of our sunglasses firm . below is correlation analysis table the results we have got from the excel

  Sales Priceadvert

expno.

households av

salesexp mean daily

Sales 1Price -0.92156 1advert exp 0.964453 -0.88466 1no. households 0.640672 -0.60117 0.594687 1av salesexp 0.048817 0.030134 0.129758 -0.27192 1mean daily 0.972855 -0.8508 0.922827 0.585831 0.015027 1

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Sales and price

As we have discussed above in graphical analysis according to law of demand there is a negative relationship between the sales and price . the Coefficient of correlation for sales and price as resulted above in the table is -0.92156.that means there is strong negative correlation between the sales and price . so if there is increase in the price there will be automatically decrease in the sales . as if the product is more expensive people are less able to spend more on sunglasses . if sunglasses price is less or we decrease from one point to another there will be significant increae in the sales .

Sales and advertising exp “Advertising is any paid-for communication overtly intended to inform and/or influence one or more people.”Jeremy Bullmore, Director, WPP

“I do not regard advertising as entertainment or an art form, but as a medium of information.”David Ogilvy ©

In simple woerds After completion of production and finishing process one important factor is to make people aware of . so ij order to make people aware of products we do marketing compaigns through print media and digital merdia .advertisment have a direct relationship with business process more we advertise more we get custumers . as we can see the results for correlation between salws and advertisement is 0.96. that is strong positive relationship . that means in order to increase sales we must increase our advertisement , if we reduce asdvertisement expenses there will be a decrease in sales as well

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Sales and no. of househoplds

it is very important factor for an enterpenuer to open a business somwehre more people are residing .in a general if an area has lot of people living there there will be a good business . correlation coefficient for sales and no. of households is 0.64 .that represents a moderate positive correlation between two variables . the reason why its moderate could bee as one family have persons of all age and tast. There are as old as young kids . so sunglasses are not really need for old people but mostly young generation are more interested in buying sunglasses as comparted to old age people .so that’s why there is moderate positive relationship

sales and average sales experience

An excellent custumer servise and experienced sales staff can make their custumers satisfied in all the possible ways . where the advertisement ends people come in store their staff’s duty starts . as there are so many factors that make a business succecfull but experienced staff has its role in order to provide all information to custumers . coeeficent of correlation for sales of sunglasses and average sales person is 0.048. as its close to 0 that means there is not really any correlation .as sales of sunglasses firm mainly depends upon the weather and people have their own choices so it doesn’t really matter a selling person should have lot of experience . there are other factors that makes people to buy sunglasses like weather , price and advertisement and mostly all products have all of the information on their own so there in not such any relationshiop between sunglasses sales and average sales person

Sales and mean daily hours

Well sunglasses business are mostly dependent on weather comditions .as weather condition in gulf countries is very hot and

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sun stays for long time , so people are most likely to have sunglasses as compare to those coumtries where it’s always cold and sun rise very rare . coefficient of correlation for sales and mean daily hours is 0.97 that means there is strong positibve relationship . sales of sunglasses is directly associated with the mean daily bhours of sunshine . more the sunshine stays more the sales and vice versa

Regression analysis What is regression analysis As we use correlation in order to measure the realationship between two variables and as a result we get a specific value that determines the strenghth of that relationship .where as regression gives us perameters in form of an equation that describes relationship and allows us to predict a value of one variable that changes from the behavior of other variable . there are two ty[pes of regression .simple linear regression where there is one dependent and one independent variable . seconde one is multiple linear regression where there is one dependent varialb and two or more independent variables .in order to carry out regression analysis we have to go through from different steps discussed as below

Step 1Dependent and independent variable

First of all we have to identify our dependent and in dependent variables I,e as sales are dependent on other varaibles such as price , advert and mean daily hours so the variables we have identified below as Sales – dependent variable Advertising expense –independent variable No of households _ independent variable Av sales experience – independent variable Mean daily hours – independent variable

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Step 2 Constructing model with the help of dependent and independent variables

As the sunglasses sales depends on price , adverts , mean daily hours etc the model could be developed as follows

\

Step 3 Formation of function Expected functoion of sales should be as follows Sales =f{Price, Advert, No households, Av sales experience and mean daily hours }

Step 4

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Finally we Are going make a regression analysis with the help of excel . by putting the data in excel we have got following results SUMMARY OUTPUT

Regression StatisticsMultiple R 0.995159046R Square 0.990341527Adjusted R Square 0.9822928Standard Error 11.0790147Observations 12

ANOVAdf SS MS F Significance F

Regression 5 75514.44927 15102.89 123.0432 5.85E-06Residual 6 736.4674003 122.7446Total 11 76250.91667

Coefficients Standard Error t Stat P-value Lower 95%Upper 95%Lower 95.0%Upper 95.0%Intercept 76.05054753 46.88243939 1.622154 0.155897 -38.6666 190.7677 -38.6666 190.7677Price -12.11445118 4.742037322 -2.55469 0.043216 -23.7178 -0.5111 -23.7178 -0.5111advert exp 1.916497655 1.061218494 1.805941 0.120953 -0.68021 4.513206 -0.68021 4.513206no. households 0.053757962 0.045210437 1.189061 0.279336 -0.05687 0.164384 -0.05687 0.164384av salesexp 0.981167294 1.341879821 0.731189 0.49222 -2.30229 4.264629 -2.30229 4.264629mean daily 13.44926356 2.863907918 4.696123 0.00334 6.441533 20.45699 6.441533 20.45699

With the help of following results we are going to define following one by one 1 Regression model 2 Goodness of fit / strength of the regression 3 interpretation of regression 4 Significance of relationships

1 Regression Model Y=a + bx Regression model is an equation that we use to predict future values based on past events Regression equation of our sunglasses firm is as follows

Sales = 76.05-12.11price+1.92advert exp +0.054 no. of households +0.98 Av sales exp+13.45Mean daily hours In order to predict any future value of sales we can use this regression model

2 Goodness of fit / Strength of the regression

Multiple R - 0.9967There is almost perfect correlation between sales and the price , advert , no of housholds ,average sales person and mean daily hours

Adjusted R square- 0.9822or 98%

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As we have more than one independent variable we will use adjusted R Square instead od R Square .so according to results we have got 98% of sales are affected by the change in price , advert expenses , mean daily hours , no of sales experience and no. of households

Significance F– 5.85E-08

At 95% level of confidence or at thye 5 % level of significance overall regression is significant

Interpretation of the regression In order to interpret regression we have to describe in terms of size and sign Our regression equation as stated above in regression model is Sales = 76.05-12.11price+1.92advert exp +0.054 no. of households +0.98 Av sales exp+13.45Mean daily hoursSales and price As there is negative correlation between sales and price that means in order to increase our sales we must reduce sunglasses price. In order to increase sales by 12.11(000) we have to decrease price by one unit

Sales and advert expenses

Coefficient of determination for sales and advert is +1.92 Advert expense . as its positive ,there is a positive relationship between sales and advert .me must increase advert expenses in order to increase sales of sunglasses .by interoperating in term of size for every unit of advert expense (000) thre is increase of sales by 1.92(000)

Sales and no. of households

As the coefficeient is =0.054 thre is a positive relationship . for every one number of household there will be an increase os 0.054(000)

Sales and average sales experience

Coefficient for sales and average sales experience ( years ) +0.98 that describs as there is positive relationship we must increase no of sales experienced staff in order to increase our sales .to increase our sales by 0.98(000) we have to increase 1 year of sales experienced person

Sales and mean daily hours Sun glasses sales and mean daily hours sunshines have direct positive relationship as the results are +13.45 that means if there is an increase of one unit of sunshine houre our sales will be increasesd by 13.45(000)

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Significance of relationships P-values ,t-stat,lower and upper 95%etc Sales and price P-value = 0.043218 that is signioficent at the 5% level Using L95% and U95% :-23.7178 and -0.5111 there is no possiblility of coming across zeroUsing t-stat:-2.5548:this satisfiea t >+2 or -2 . as the results satisfies so its significant

Sales and advert expenses P-value = 0.1209 that is signioficent at the 5% level Using L95% and U95% :-0.6802 and 4.5132 there is no possiblility of coming across zeroUsing t-stat:1.8059:this satisfiea t >+2 or -2 . as the results satisfies so its significant Sales and no of households P-value = 0.2793 that is signioficent at the 5% level Using L95% and U95% :-0.05687 and 0.16438 there is no possiblility of coming across zeroUsing t-stat:1.1890:this satisfiea t >+2 or -2 . as the results satisfies so its significant Sales and average sales experienceP-value = 0.4922 that is signioficent at the 5% level Using L95% and U95% :-2.3022 and 4.2646 there is no possiblility of coming across zeroUsing t-stat:0.7311:this satisfiea t >+2 or -2 . as the results satisfies so its significant Sales and mean daily hours P-value = 0.00334 that is signioficent at the 5% level Using L95% and U95% :6.4415 and 20.4569 there is no possiblility of coming across zeroUsing t-stat:4.6961:this satisfiea t >+2 or -2 . as the results satisfies so its significant

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Conclusion and recommendationConclusion As we have carried out different analysis on sales and its ecpenditures through various ways , we have came to know about that sales really associated with some of factors that are incolved in our firm .as we carrreid out diagrammatic presentation we realized as sales is mostly concerned with its price and advertising expenses . where as sales experience is concerned it doesn’t really count towards sales as a major but that is important in order to provide custumers all of the relevant information . moving forward to correlation coefficient we came to know some of the parameters have strong relationship with sales . so in order to increase sales of saunglasses price , advert expenses , mean daily hours of sunshine are very important factors to considerate whereas no of households and average sales experience have very moderate relationship with sales . furthermore regression analysis gave us a regression equation model . on the basis of whole years sales and expenses record we came to know dependency of sales on independent variables such as price, advert , mean daily hours etc . and with the help of regression equation we have got parameters in what extent to increase our sales we have to change in independent variables .Recommendation As we have got an idea about different kind of variables how do they affect its sales . in my opinion sales of sunglasses is mostly effected by the weather condition . so months(june , july, august , September ) with more sunshine hours we must do more advertising and reduce the price in order to capture the growth market and in order to make out price strategy affected where as I don’t think so we have to make more advert expenses in the start and end of the year .

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Bibliography

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refrences 1 CURWIN AND SLATTER

2 http://www.surveysystem.com/correlation.htm

3Curwin and slatter page 410

4Elementary statistics Mario f triola