Price Elasticity Model

Assumptions

• Assume a retailer is skeptical about pricing his product due to heavy traffic & competition exists in the market
• Retailer expects the Data-Scientist to enlist recommendations(optimum price) to price his products. Lets say “DSLR-Camera”
• Lets consider the un-named columns as “Sales units”,“Own Price”,“Competitor-1 price”,“Competitor-2 price”
• Dependent variable as “Sales” and Independent variables as “Own Price”,“Competitor-1 price”,“Competitor-2 price”

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Research question : Retailer wants to optimize his price based on the existing competition

Hypothesis: Is there any significant relationship between Sales & other variables

Null Hypothesis: There is NO significant relationship between Sales & other variables

Alternate Hypothesis: There is significant relationship between Sales & other variables

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Distribution of Variables : Histogram

• Exploratory data analysis to understand the distribution(normal/skewed) of variables

   vars    n    mean      sd median trimmed    mad  min   max range skew kurtosis     se
X1    1 2650 9694.15 5375.79   6997 8325.35 689.41 6450 28973 22523 2.17     3.93 104.43

Insigths

• Distribution of Sales Volume is right skewed by 2.17. Higher sales volume of camera has lower density

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   vars    n     mean     sd median trimmed    mad   min   max range skew kurtosis    se
X1    1 2650 26541.64 675.58  26463 26549.7 690.89 25140 27904  2764 0.02    -0.74 13.12

Insigths

• Distribution of Own price is normally distributed. Prices of camera is symmetric

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   vars    n     mean     sd median trimmed    mad     min   max  range  skew kurtosis    se
X1    1 2650 32209.15 704.84  32369 32376.9 220.91 28126.5 32609 4482.5 -3.76    14.29 13.69

Insigths

• Distribution of Comp1 price is left skewed by -3.76. Lower price of camera has lower density

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   vars    n     mean   sd  median  trimmed   mad   min   max range skew kurtosis   se
X1    1 2650 32781.58 8.45 32780.5 32781.36 11.12 32750 32805    55 0.17    -0.28 0.16

Insigths

• Distribution of Comp2 price is normally disributes. Comp2 Prices of camera is symmetric

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Distribution of Variables(Transformation) : Histogram

   vars    n    mean      sd median trimmed    mad  min   max range skew kurtosis    se
X1    1 2650 8065.11 1823.71   6997 7802.11 689.41 6450 12228  5778 0.87     -0.7 35.43

Insigths

• Distribution of Sales Volume volume is normally disributed. Transformation successful.

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   vars    n     mean     sd median  trimmed    mad   min   max range skew kurtosis   se
X1    1 2650 32382.42 148.77  32369 32385.01 220.91 32009 32609   600 -0.1    -1.32 2.89

Insigths

• Distribution of Comp1 price is normally disributed. Transformation successful.

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Relationship between Variables : Scatterplot

Insigths

• Sales volume & Own price are weekly negatively correlated

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Insigths

• Sales volume & Comp1 price are fairly positively correlated

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Insigths

• Sales volume & Comp2 price are weekly negatively correlated

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Relationship between Variables : Correlation Analysis

                      sales  own_price comp1_price comp2_price    sal_std comp1_price_std
sales            1.00000000 -0.3509908   0.1109078  -0.2072594  0.6101745     -0.02732503
own_price       -0.35099084  1.0000000   0.1895046   0.6158865 -0.1356289      0.54362935
comp1_price      0.11090783  0.1895046   1.0000000   0.1350718  0.2066278      0.49750120
comp2_price     -0.20725945  0.6158865   0.1350718   1.0000000 -0.1057077      0.34547193
sal_std          0.61017451 -0.1356289   0.2066278  -0.1057077  1.0000000      0.39029220
comp1_price_std -0.02732503  0.5436293   0.4975012   0.3454719  0.3902922      1.00000000

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Linear Regression

Stratified Random Sampling

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Elasticity Model

Call:
lm(formula = log(sal_std) ~ log(own_price) + log(comp1_price_std) + 
    log(comp2_price), data = Terra_Blue_XT_Aggr)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.23248 -0.13791 -0.05592  0.13321  0.62873 

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)          146.7774   171.8137   0.854   0.3930    
log(own_price)        -3.8358     0.1883 -20.369   <2e-16 ***
log(comp1_price_std)  30.3929     0.8760  34.696   <2e-16 ***
log(comp2_price)     -39.8529    16.6185  -2.398   0.0165 *  
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Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1737 on 2646 degrees of freedom
Multiple R-squared:  0.3253,    Adjusted R-squared:  0.3245 
F-statistic: 425.3 on 3 and 2646 DF,  p-value: < 2.2e-16

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Confidence Intervals

                       2.5 %      97.5 %
(Intercept)      -397.796771 1077.619866
log(own_price)     -6.081026   -4.623187
log(comp1_price)    3.132422    4.423571
log(comp2_price) -101.742746   41.049729

Insights

• Since p<0.05, we reject Null Hypothesis & conclude that there is a significant relationship between Sales volume, Own price, Comp1 price and Comp2 price

• Own Price, Comp1 price & Comp2 price has significant evidence in estimating sales volume.

• ~32% of variation is explained by the model & has significant evidence in explaining it

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