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1 University f Tennessee, Knxville Trace: Tennessee Research and Creative Exchange University f Tennessee Hnrs Thesis Prjects University f Tennessee Hnrs Prgram Sales Analysis David Mark Shuler University f Tennessee - Knxville Fllw this and additinal wrks at: Recmmended Citatin Shuler, David Mark, "Sales Analysis" (2007). University f Tennessee Hnrs Thesis Prjects. This is brught t yu fr free and pen access by the University f Tennessee Hnrs Prgram at Trace: Tennessee Research and Creative Exchange. It has been accepted fr inclusin in University f Tennessee Hnrs Thesis Prjects by an authrized administratr f Trace: Tennessee Research and Creative Exchange. Fr mre infrmatin, please cntact trace@utk.edu.

2 Sales Analysis David Shuler and Charles Cwiek Senir Hnrs Prject, UH 499

3 The purpse f this prject is t analyze real data cllected frm my summer as a bk salesman. Regressin is a fascinating and useful way t find ut exactly what might be causing a desired utcme. As is the case with mst sales, "Units Sld" is the desired utcme, and whatever makes it increase is f interest t the salespersn and his cmpany. Since Charlie Cwiek isn't the nly ne that will be reading this, I will begin with a brief descriptin in as plain English as I can manage. The dependent variable, r the variable which is believed t be changed by the ther variables, is Units Sld. All the ther variables are Independent, meaning they are allwed t naturally vary, and they nly affect the dependent variable. Regressin discvers exactly hw much variatin in the independent variables explains variatin in the dependent variable. I have used tw types f independent variables: numeric and nminal. The numeric variables are as fllws: Experience - hw many days f selling I have finished Units Sld n Previus Day - hw many units I sld the day befre Dr Dems - hw many demnstratins I perfrmed standing up utside at the dr each day Sit Dwns - hw many demnstratins perfrmed sitting dwn each day High Temperature - the temperature as I read it in my car between 3:30PM and 4:00PM Numeric variables are just that, they are cntinuus numbers that in this case have n upper limit. Yu can perfrm arithmetic functins n them like adding and subtracting ( + = 2). The nminal variables. n the ther hand, are categrical. Each categry is either a number r wrd, but the numbers are nt the same as the numeric variables, since yu can't add them r d any kind f math with them ( + NOT = 2). They are just a name that represents a grup. The categrical variables are as fllws: Kncked befre 8 AM: 0 = YES, = NO Time Left Last Huse: 0 befre 9:30PM, = after 9:30PM but befre 0PM, 2 = after 0PM Shirt Style: either Pl r T, whichever was wrn that day Shirt Clr: describes the clr r shirt wrn that day Hair: Flat r Spiked Shrts Clr: describes the clr f shrts wrn that day Clgne: 0 = n, = yes

4 Rained: 0 = n, = yes Time t Bed: = befre :OOPM, 2 = after :OOPM but befre midnight, 3 = after midnight Talked n Phne Previus Night: 0 = n, = yes Befre fitting a mdel that describes the dependent variable (Units Sld) as a functin f the independent variables, I have t d a few tests t make sure the mdel will yield accurate results. First and mst bvius is t make sure that the data I have entered is crrect. Typs are a great way t make yur results cmpletely wrng. If I sld 06 units ne day, but I accidentally typed 60 that wuld skew my mdel. The first way t crrect these errrs is t just eyeball it. Hwever, a mre advanced methd f checking yur data is make distributins f them. S the fllwing pages are distributins f each variable, cmplete with minimums and maximums, means and number f entries, which aids in the checking prcess. Fr instance, in Shirt Clr, the histgram shws hw ften each shirt clr is entered. Previusly, it shwed that in ne case I typed Bleu instead f Blue, which wuld have messed up my mdel. I fixed all the typs and printed ut the belw.

5 Distributins Day f Week Frequencies Level Cunt Ttal 66 Prb N Missing 0 6 Levels Experience Quantiles 00.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 0.0% 2.5% 0.5% 0.0% minimum

6 Mments Mean Std Dev Std Err Mean upper 95% Mean lwer 95% Mean N Units Sld r----l-..., 50 Quantiles 00.0% maximum 99.5% 97.5% 90.0% 75.0% quartile 50.0% median 25.0% quartile 0.0% 2.5% 0.5% 0.0% minimum Mments Mean Std Dev Std Err Mean upper 95% Mean lwer 95% Mean N

7 Units Sld n Previus Day L...r-...I 50 O-+----~ Quantiles 00.0% maximum % % % % quartile % median % quartile % % % % minimum 0.00 Mments Mean Std Oev Std Err Mean upper 95% Mean lwer 95% Mean N 66

8 r Dr Dems 25 Quantiles 00.0% maximum % % % % quartile % median % quartile % % % % minimum Mments Mean Std Dev Std Err Mean upper 95% Mean lwer 95% Mean N 66

9 /. Sit Dwns 20 ~~... " 5 0 [ 5 Quantiles 00.0% maximum % % % % quartile % median % quartile % % % % minimum Mments Mean Std Dev Std Err Mean upper 95% Mean !wer 95% Mean N 66

10 ..... Kncked Befre 8AM ~ - 0 Frequencies Level Ttal N Missing 2 Levels Cunt Prb Time Left Last Huse '-- Frequencies Level 2 Ttal N Missing 3 Levels Cunt Prb

11 , " Shirt Style T - " Pl I' I,,, Frequencies Level Cunt Prb Pl T Ttal N Missing 0 2 Levels Shirt Clr White Red Stripe Light Blue Gray Blue/Brwn Blue Stripe Blue Frequencies Level Cunt Prb Blue Blue Stripe Blue/Brwn Gray Light Blue Red Stripe White Ttal N Missing 3,7levels

12 ,. Hair : Spiked - : ", Flat Bandana Frequencies Level Bandana Flat Spiked Ttal N Missing 3 Levels Shrts Clr Cunt Prb Gray Blue Frequencies Level Blue Gray Green Khaki Ttal N Missing 4 Levels Cunt Prb

13 Clgne Frequencies Level Ttal N Missing 2 Levels Time T Bed Cunt Prb Frequencies Level 2 3 Ttal N Missing 3 Levels Cunt Prb

14 Talked n Phne Previus Night - Ii I... 0 Frequencies Level Ttal N Missing 2 Levels Rained Cunt Prb rj.,. Frequencies Level Ttal N Missing 2 Levels Cunt Prb

15 High Tempterature [ Quantiles 00.0% 99.5% 97.5% 90.0% 75.0% 50.0% 25.0% 0.0% 2.5% 0.5% 0.0% Mments maximum quartile median quartile minimum Mean Std Dev Std Err Mean upper 95% Mean lwer 95% Mean N

16 The ther preliminary test I perfrmed n my data was a test fr clinearity amng the numeric independent variables. Clinearity means that the variables are related s much that yu shuld just put ne f them in the mdel. In rder t test this, I made a scatterplt matrix. Yu can lk at the crrelatin cefficients fr each set f variables in the table belw. If a value is clse t r -, that indicates strng clinearity, and yu shuld remve ne f the variables. Yu can als lk at the plts and eyeball them t see if there seems t be sme relatinship. This culd discver a relatinship that the crrelatin cefficients wuld nt pick up, since the crrelatin cefficients nly describe linear relatinships. Multivariate Crrelatins Experience Units Sld n Dr Dems Sit Dwns High Tempterature Previus Day Experience Units Sld n Previus Day Dr Dems Sit Dwns High Tempterature

17 Scatter lt Matrix (U Experience /....,:. rr r# III.. :.i.: ':,ii L ':. - trl'..:...- \...:~. I ri' Unit$ Sld n PrevIus Day Dr Dems As yu can see, [dr dems I experience] and [high temperature I experience] have the highest cefficients and their graphs indicate sme weak relatinship. Hwever, since I think it is imprtant that all thse variables be in the mdel, and the cefficients are nt t clse t + r -, I will leave all the variables in the mdel. It makes sense that experience and high temperature are related because as the summer went alng it became htter, and as mre time passed I gt mre experience.

18 S nw it's time t actually run a mdel. In the Y (dependent) psitin is Units Sld, and all the rest f the variables are placed in the X (independent) psitin. JMP (the statistical sftware that I used) prduces a lt f utput fr mdels, especially multivariate nes, but I will emphasize the imprtant parts. The Rsquared value indicates hw much f the variatin in Units Sld is explained by the mdel, r hw much is explained by all the independent variables. As yu can see, 74% f the variatin in Units Sld is explained by this mdel. The mst imprtant part f the data is the effects test. This says hw imprtant each variable is in explaining the variatin in units sld. Fr each independent variable, the prbability f seeing as strng a relatinship between that variable and Units Sld in the data, if in fact there is n relatinship, is the p- value, s a lw p-value means that we are pretty sure the variable is related t Units Sld. S, lking at the p-values (Prb > F clumn), we can say with certainty that Sit Dwns, Time Left Last Huse, and Talked n Phne Previus Night are strngly related t Units Sld. We can als see that Units Sld n Previus Day, Shirt Style, Shirt Clr, Rained, High Temperature, and Shrts Clr are really clse t the cutff. Using the parameter estimates, we can see that the relatinship between Sit Dwns and Units Sld is psitive, s as Sit Dwns increases, s des Units Sld. The same is true fr Time Left Last Huse and Talked n Phne Previus Night; n nights when I left the last huse after 0PM, I sld mre units, and when I talked n the phne the night befre, Units Sld als increased. One pssible cause fr this wuld be that I had a better attitude when I talked n the phne the night befre. Summary f Fit RSquare RSquare Adj Rt Mean Square Errr Mean f Respnse Observatins (r Sum Wgts) Analysis f Variance Surce DF Mdel 30 Errr 3 Sum f Squares Mean Square F Rati Prb>F

19 Surce DF Sum f Squares Mean Square F Rati C. Ttal Parameter Estimates Term Estimate Std Errr t Rati Prb>ltl Intercept Day f the Week[J Day f the Week[2J Day f the Week[3] Day f the Week[4J Day f the Week[5] Experience Units Sld n Previus Day Dr Dems Sit Dwns Kncked Befre BAM [OJ Time Left Last Huse 2[0] Time Left Last Huse 2[J Shirt Style[Pl] Shirt Clr[Blue] Shirt Clr[Blue Stripe] Shirt Clr[Blue/Brwn] Shirt Clr[Gray] Shirt Clr[Light Blue] Shirt Clr[Red Stripe] Hai r[bandana] Hair[Flat] Shrts Clr[Blue] Shrts Clr[Gray] Shrts Clr[Green] Clgne[O] Time T Bed[] Time T Bed[2] Talked n Phne Previus Night[O] Rained[O] High Tempterature Effect Tests Surce Nparm DF Sum f Squares F Rati Prb> F Day f the Week Experience Units Sld n Previus Day Dr Dems Sit Dwns Kncked Befre 8AM Time Left Last Huse Shirt Style Shirt Clr Hair Shrts Clr Clgne Time T Bed Talked n Phne Previus Night Rained High Tempterature

20 LS Means Plt 250~ ~ "0 ~ 00 '0 r (fj Q.) 50.!!3::E '2 en 0 ~ ~ ~------~ ~ 2 Time Left Last Huse 2 LS Means Plt 250, ~ "0 ~ '0 00- en r - Q.) 50-.!!3 ::E '2 (fj 0- ~ ~ I Talked n Phne Previus Night Nw that we have a rugh idea f which variables are significant, I am ging t try t fit a mdel that cntains nly thse imprtant nes. I will start with the full mdel and add the 2-level interactins f the numeric variables t see if ne variable might be imprtant nly if anther is present. Here is the riginal mdel: Summary f Fit RSquare RSquare Adj Rt Mean Square Errr Mean f Respnse Observatins (r Sum Wgts) Analysis f Variance Surce DF Mdel 40 Errr 2 C. Ttal 6 Sum f Squares Mean Square F Rati Prb> F Parameter Estimates Term Intercept Day f the Week[] Day f the Week[2] Day f the Week[3] Day f the Week[4] Day f the Week[5] Experience Units Sld n Previus Day Dr Dems Sit Dwns Kncked Befre 8AM[0] Time Left Last Huse 2[0] Time Left Last Huse 2[] Shirt Style[Pl] Estimate Std Errr t Rati Prb>ltl

21 Term Estimate Std Errr t Rati Prb>ltl Shirt Clr[Blue] Shirt Clr[Blue Stripe] Shirt Clr(Blue/Brwn] Shirt Clr[Gray] Shirt Cir[Light Blue] Shirt Clr[Red Stripe] Hair[Bandana] Hair[Flat] Shrts Clr[Blue] Shrts Clr[Gray] Shrts Clr[Green] Clgne[O] Time T Bed[] Time T Bed[2] Talked n Phne Previus Night[O] Rained[O] High Tempterature (Experience )*(Units Sld n Previus Day ) (Experience )*(Dr Dems-2.758) (Experience )*(Sit Dwns-.387) (Experience )*(High Tempterature ) (Units Sld n Previus Day )*(Dr Dems-2.758) (Units Sld n Previus Day )*(Sit Dwns-.387) (Units Sld n Previus Day )*(High Tempterature ) (Dr Dems-2.758)*(Sit Dwns-.387) (Dr Dems )*(High Tempterature ) (Sit Dwns-.387 )*(High Tempterature ) Effect Tests Surce Nparm DF Sum f Squares F Rati Prb> F Day f the Week Experience Units Sld n Previus Day Dr Dems Sit Dwns * Kncked Befre 8AM Time Left Last Huse Shirt Style Shirt Clr Hair Shrts Clr Clgne * Time T Bed Talked n Phne Previus Night * Rained * High Tempterature Experience*Units Sld n Previus Day Experience*Dr Dems Experience*Sit Dwns Experience*High Tempterature e Units Sld n Previus Day*Dr Dems " Units Sld n Previus Day"Sit Dwns Units Sld n Previus Day"High T empterature Dr Dems*Sit Dwns Dr Dems*High Tempterature * Sit Dwns*High Tempterature

22 The effects with an asterisk beside them were significant enugh t be put int the new mdel. Here is the new mdel with nly the significant variables. Since tw f the imprtant effects are interactin terms, I had t include bth f the cmpnents individually as well, even thugh alne they are nt significant: Summary f Fit RSquare RSquare Adj Rt Mean Square Errr Mean f Respnse Observatins (r Sum Wgts) Analysis f Variance Surce DF Mdel 9 Errr 55 C. Tml 64 Sum f Squares Mean Square F Rati Prb> F Parameter Estimates Term Intercept Clgne[O] Talked n Phne Previus Night[O] Rai ned [0] Units Sld n Previus Day Dr Dems Sit Dwns High Tempterature (Dr Dems )*(High Tempterature ) (Units Sld n Previus Day )*(Dr Dems ) Estimate Std Errr t Rati Prb>ltl Effect Tests Surce Clgne Talked n Phne Previus Night Rained Units Sld n Previus Day Dr Dems Sit Dwns High Tempterature Dr Dems*High Tempterature Units Sld n Previus Day*Dr Dems Nparm DF Sum f Squares F Rati Prb>F * * * * Yu can see that sme f the effects we riginally thught were significant turned ut t be insignificant when separated frm the cmplete mdel. Once mre, I will fit anther new mdel with nly the imprtant effects: Summary f Fit RSquare RSquare Adj Rt Mean Square Errr Mean f Respnse Observatins (r Sum Wgts) Analysis f Variance Surce DF Sum f Squares Mean Square F Rati

23 Surce OF Sum f Squares Mean Square F Rati Mdel Errr Prb> F C. Ttal Parameter Estimates Term Estimate Std Errr t Rati Prb>ltl Intercept Sit Dwns Dr Dems Talked n Phne Previus Night[O] Rained[O] (Dr Dems-2.697)*(High Tempterature ) High Tempterature Effect Tests Surce Nparm OF Sum f Squares F Rati Prb>F Sit Dwns Dr Dems Talked n Phne Previus Night Rained Dr Dems*High Tempterature High T empterature Predictin Prfiler "0 N 0> '0 N N (J) lo ~ l() ~ ("') 0 9 'c r-.: N :J lo N +I lo 0 lo 0 lo 0 lo 0 I.{) 0 0 I.{) 0 lo 0 I.{) N N N ex) 0> 0> Talked n Phne 0 High Sit Dwns Dr Dems Previus Night Rained Tempterature "'" "0 I.{) '0 ~ ("') (J) lo 0 N 9 r-- t.ri 'c r-- N "'" 00 :J ~ +I 0 lo 0 I.{) 0 I.{) 0 I.{) 0 I.{) 0 0 I.{) 0 I.{) 0 I.{) N N N ex) 0> 0> 0 0, Talked n Phne 0 High Sit Dwns Dr Dems Previus Night Rained Tempterature "0 ill r '0 -.;t lo (J) 0> N 9 'c ("') r N "'" r :J I.{) + 0 lo 0 I.{) 0 I.{) 0 lo 0 I.{) 0 0 N N N Talked n Phne 0 High Sit Dwns Dr Dems Previus Night Rained T empterature

24 This time, all the effects in the mdel are imprtant. Using the predictin prfiler is anther way we can determine the directin f each relatinship. Sit Dwns is psitive, as we stated earlier. Rained is als psitive, meaning that if it rained I sld mre units. One pssible reasn that Rained wuld be psitive is that my attitude was better when it rained because it was much cler. Als, yu tend t get mre sympathy sales when yu're dripping wet. Talked n Phne Previus Night was psitive, prbably because my attitude was better. Nw the crssed effect Dr Dems*High Temperature is hard t explain. As yu can see in the first predictin prfiler, when High Temperature is at 03, the slpe f Dr Dems is upward slping, meaning there is a psitive relatinship between it and Units Sld. Hwever, in the secnd prfiler, when High Temperature is lw, 9.5, the slpe f Dr Dems is decreasing, meaning dr dems is negatively related t Units Sld if the Temperature is lw. In the third prfiler, when High Temperature is at a medium level, there is n relatinship. This makes n sense because mre dems shuld always mean mre sales, regardless f the weather. Smetimes with real data, especially with small sample sizes, there are unexplained interactins that just dn't make physical sense. My guess is with mre data, we prbably wuld nt see this interactin. The next test I perfrmed was t test a thery presented t me by my sales manager. He said mst salespeple's Units Sld have a parablic shape ver the curse f the summer. His reasning was that yu start ff "stupid," but yur attitude is great s yu wrk really hard. As the summer prgresses, yur attitude becmes wrse, but yur skill imprves. S the middle f the summer is where mst peple peak, since the cmbinatin f gd attitude and skill is greatest at that pint. After that, yur attitude starts t get s bad that yur units sld starts t decline. I decided t test this thery. The Experience variable represents the number f days I had sld, s I fir a mdel with Experience (a linear cmpnent) and Experience * Experience (a quadratic cmpnent) as the independent variables (Units Sld still being the dependent variable) in rder t get a plt f Units Sld ver Time. The results were exactly like my manager said, an umbrella shape. Since the p-value fr the quadratic term is <.05, we can say that the quadratic, nn-linear relatinship that my bss said wuld exist des appear in my data. The regressin plt belw illustrates the umbrella-shape described by my bss. Hwever, even thugh the p-value fr the quadratic term is statistically Significant, yu can see there is a lt f variatin arund the curved line f predictin. And when these tw terms were added t my previus mdel (analysis nt

25 shwn here), they were nt statistically significant. S, althugh my bss' thery was crrect, this umbrella effect was nt as imprtant in predicting Units Sld as the ther variables previusly discussed. Even thugh the trend is present, it is nt as helpful in predicting Units Sld as the previus 5 variables were. Respnse Units Sld Whle Mdel Re ressin Plt ~ 200 :250 (f) rj) ~ 00 ::::> ~ Experience Summary f Fit RSquare RSquare Adj Rt Mean Square Errr Mean f Respnse Observatins (r Sum Wgts) Analysis f Variance Surce OF Mdel 2 Errr 63 C. Ttal 65 Sum f Squares Mean Square F Rati Prb>F Parameter Estimates Term Intercept Experience (Experience-33.5)*(Experience-33.5) Estimate Std Errr t Rati Prb>ltl < S far we have determined which variables are imprtant in predicting Units Sld, and we have tested my bss' thery that Units Sld will be umbrella-shaped ver time. When we were pulling ut variables that were imprtant, Sit Dwns were always at the tp f the list. This supprts my bss' idea that selling is a numbers game, and the mre peple yu give an pprtunity t buy, the mre sales yu will get. But that raises the questin, "Hw d I get mre Sit Dwns?" In rder t answer that questin, I

26

27 will fit anther mdel, but this time I will put Sit Dwns in the Y psitin. My bss' thery! again, is that it is a numbers game, and the mre drs yu knck n, the mre sit dwns yu will have, and the mre sit dwns, the mre sales. Every huse I kncked n where smene was hme was either a sit dwn r dr dem, s sit dwns + dr dems = ttal drs kncked n. A dr dem was dne ONLY if the prspect wuld nt allw me t sit dwn with them. Here are the results: Summary f Fit RSquare RSquare Adj Rt Mean Square Errr Mean f Respnse Observatins (r Sum Wgts) Analysis f Variance Surce DF Mdel 29 Errr 32 C. Ttal 6 Sum f Squares Mean Square F Rati.0580 Prb>F Parameter Estimates Term Intercept Day f the Week[] Day f the Week[2] Day f the Week[3] Day f the Week[4] Day f the Week[5] Experience Units Sld n Previus Day Kncked Befre 8AM[0] Time Left Last Huse 2[0] Time Left Last Huse 2[] Shirt Style[Pl] Shirt Clr[Blue] Shirt Clr[Blue Stripe] Shirt Clr[Blue/Brwn] Shirt Clr[Gray] Shirt Clr[Ught Blue] Shirt Clr[Red Stripe] Hair[Bandana] Hair[Flat] Shrts Clr[Blue] Shrts Clr[Gray] Shrts Clr[Green] Clgne[O] Time T Bed[] Time T Bed[2] Talked n Phne Previus Night[O] Rained [0] High Tempterature Dr Dems Estimate Std Errr t Rati Prb>ltl Effect Tests Surce Day f the Week Experience Units Sld n Previus Day Dr Dems Nparm 5 DF 5 Sum f Squares F Rati Prb> F

28 Surce Nparm DF Sum f Squares F Rati Prb > F Kncked Befre8AM Time Left Last Huse Shirt Style Shirt Clr Hair Shrts Clr Clgne Time T Bed Talked n Phne Previus Night Rained High Tempterature As yu can see, Dr Dems was the mst imprtant factr in getting Sit Dwns, but the relatinship is negative, meaning as Dr Dems increases, Sit Dwns decrease. That makes sense, because there are nly s many hurs t wrk, s if yu fill them up with dr dems, yu wn't have as many sit dwns. High Temperature was als an imprtant factr. My reasning fr that is that peple feel srry fr a cllege by standing utside in blazing ht weather, and they are mre apt t let ~Iim in under such cnditins. Experience and Clgne als affected whether r nt peple let me in, which makes sense because Clgne makes yu mre pleasant, and Experience adds skill in cnvincing peple t let yu in. In clsing, I wuld like t prvide sme advice t new salespeple. First f all, Sit Dwns are the mst imprtant factr in increasing yur sales. As we saw, filling yur day up with dr dems will decrease yur sit dwns, s be mre aggressive and try t get in the huse mre than nce in trying t get in the huse. Anther wrd f wisdm is wrk thrugh bad weather. As we saw, sales increased n days when it rained, whether it was ut f sympathy r I just had a better attitude in the rain, sales went up, s wrk in the rain. Als, if it is ht utside, wrk anyway! Dr dems are mre likely t becme sales in ht weather, s wrk thrugh that as well. Lastly, d whatever it takes t keep a gd attitude. Sales managers will tell yu that selling is transference f feeling, and it's true! Be happy and have a gd attitude and yu will sell mre. Fr me, it was talking n the phne the night befre, but fr yu it culd be smething else. Just stay psitive.