The data set contains the results for a price experiment for an item that is is sold online. For each day in the data set the price, the sales (i.e. realized demand), the potential sales (based on click data) is recorded. There are also a number of other features: days of the week, a direct competitors price and weather status (rainy or not). Make sure that you divide the data into a training set (around 75 %) and a test set (around 25) Day,Sales,Price,Potential_Demand,Sat,Sun,Mon,Tue,Wed,Thu,Rain,Compatitors_Price 1-Jan-22,100,97,128,1,0,0,0,0,0,1,100 2-Jan-22,63,98,87,0,1,0,0,0,0,0,100 3-Jan-22,38,100,50,0,0,1,0,0,0,0,100 4-Jan-22,41,101,55,0,0,0,1,0,0,0,100 5-Jan-22,48,103,69,0,0,0,0,1,0,0,100 6-Jan-22,55,104,84,0,0,0,0,0,1,1,100 7-Jan-22,71,106,105,0,0,0,0,0,0,1,100 8-Jan-22,50,107,85,1,0,0,0,0,0,0,100 9-Jan-22,41,109,71,0,1,0,0,0,0,0,100 10-Jan-22,39,107,62,0,0,1,0,0,0,0,100 11-Jan-22,52,106,75,0,0,0,1,0,0,0,100 12-Jan-22,37,104,59,0,0,0,0,1,0,0,100 13-Jan-22,65,103,93,0,0,0,0,0,1,1,100 14-Jan-22,53,101,69,0,0,0,0,0,0,0,100 15-Jan-22,52,100,72,1,0,0,0,0,0,0,100 16-Jan-22,54,98,72,0,1,0,0,0,0,0,100 17-Jan-22,35,97,45,0,0,1,0,0,0,0,100 18-Jan-22,32,98,39,0,0,0,1,0,0,0,100 19-Jan-22,46,100,64,0,0,0,0,1,0,0,100 20-Jan-22,70,101,98,0,0,0,0,0,1,1,100 21-Jan-22,38,103,51,0,0,0,0,0,0,0,100 22-Jan-22,63,104,89,1,0,0,0,0,0,0,100 23-Jan-22,75,106,113,0,1,0,0,0,0,1,100 24-Jan-22,27,107,46,0,0,1,0,0,0,0,100 25-Jan-22,38,109,67,0,0,0,1,0,0,0,100 26-Jan-22,33,107,52,0,0,0,0,1,0,0,100 27-Jan-22,36,106,54,0,0,0,0,0,1,0,100 28-Jan-22,48,104,68,0,0,0,0,0,0,0,100 29-Jan-22,60,103,84,1,0,0,0,0,0,0,100 30-Jan-22,65,101,90,0,1,0,0,0,0,0,100 31-Jan-22,50,100,68,0,0,1,0,0,0,0,100 1-Feb-22,47,98,65,0,0,0,1,0,0,0,100 2-Feb-22,33,97,44,0,0,0,0,1,0,0,100 3-Feb-22,47,98,64,0,0,0,0,0,1,0,100 4-Feb-22,51,100,65,0,0,0,0,0,0,0,100 5-Feb-22,65,101,90,1,0,0,0,0,0,0,100 6-Feb-22,69,103,97,0,1,0,0,0,0,0,100 7-Feb-22,51,104,74,0,0,1,0,0,0,0,100 8-Feb-22,37,106,58,0,0,0,1,0,0,0,100 9-Feb-22,32,107,49,0,0,0,0,1,0,0,100 10-Feb-22,29,109,46,0,0,0,0,0,1,0,100 11-Feb-22,31,110,50,0,0,0,0,0,0,0,100 12-Feb-22,67,97,87,1,0,0,0,0,0,0,100 13-Feb-22,67,98,85,0,1,0,0,0,0,0,100 14-Feb-22,51,100,72,0,0,1,0,0,0,0,100 15-Feb-22,27,101,39,0,0,0,1,0,0,0,100 16-Feb-22,42,103,55,0,0,0,0,1,0,0,100 17-Feb-22,52,104,73,0,0,0,0,0,1,0,100 18-Feb-22,24,106,39,0,0,0,0,0,0,0,100 19-Feb-22,57,107,92,1,0,0,0,0,0,0,100 20-Feb-22,50,109,76,0,1,0,0,0,0,0,100 21-Feb-22,47,107,70,0,0,1,0,0,0,0,100 22-Feb-22,32,106,52,0,0,0,1,0,0,0,100 23-Feb-22,49,104,73,0,0,0,0,1,0,1,100 24-Feb-22,42,103,61,0,0,0,0,0,1,0,100 25-Feb-22,41,101,55,0,0,0,0,0,0,0,100 26-Feb-22,60,100,80,1,0,0,0,0,0,0,100 27-Feb-22,53,98,73,0,1,0,0,0,0,0,100 28-Feb-22,47,97,61,0,0,1,0,0,0,0,100 1-Mar-22,47,98,63,0,0,0,1,0,0,0,90 2-Mar-22,38,100,53,0,0,0,0,1,0,0,90 3-Mar-22,34,101,45,0,0,0,0,0,1,0,90 4-Mar-22,38,103,51,0,0,0,0,0,0,0,90 5-Mar-22,102,96,127,1,0,0,0,0,0,1,90 6-Mar-22,53,114,96,0,1,0,0,0,0,0,90 7-Mar-22,22,106,36,0,0,1,0,0,0,0,90 8-Mar-22,41,114,75,0,0,0,1,0,0,1,90 9-Mar-22,72,95,89,0,0,0,0,1,0,1,90 10-Mar-22,64,102,96,0,0,0,0,0,1,1,90 11-Mar-22,26,104,35,0,0,0,0,0,0,0,90 12-Mar-22,82,98,105,1,0,0,0,0,0,1,90 13-Mar-22,45,109,76,0,1,0,0,0,0,0,90 14-Mar-22,46,112,76,0,0,1,0,0,0,0,90 15-Mar-22,73,97,93,0,0,0,1,0,0,1,90 16-Mar-22,39,102,57,0,0,0,0,1,0,0,90 17-Mar-22,38,107,63,0,0,0,0,0,1,0,90 18-Mar-22,46,96,59,0,0,0,0,0,0,0,90 19-Mar-22,71,109,121,1,0,0,0,0,0,1,90 20-Mar-22,79,107,130,0,1,0,0,0,0,1,90 21-Mar-22,45,102,64,0,0,1,0,0,0,0,90 22-Mar-22,42,107,69,0,0,0,1,0,0,0,90 23-Mar-22,27,114,56,0,0,0,0,1,0,0,90 24-Mar-22,57,107,87,0,0,0,0,0,1,1,90 25-Mar-22,48,103,72,0,0,0,0,0,0,0,90 26-Mar-22,56,107,88,1,0,0,0,0,0,0,90 27-Mar-22,34,107,56,0,1,0,0,0,0,0,90 28-Mar-22,44,101,61,0,0,1,0,0,0,0,90 29-Mar-22,34,106,53,0,0,0,1,0,0,0,90 30-Mar-22,46,101,65,0,0,0,0,1,0,0,90 31-Mar-22,39,103,56,0,0,0,0,0,1,0,90 1-Apr-22,39,107,60,0,0,0,0,0,0,0,110 2-Apr-22,96,95,119,1,0,0,0,0,0,1,110 3-Apr-22,40,110,70,0,1,0,0,0,0,0,110 4-Apr-22,44,100,58,0,0,1,0,0,0,0,110 5-Apr-22,45,102,64,0,0,0,1,0,0,0,110 6-Apr-22,34,97,43,0,0,0,0,1,0,0,110 7-Apr-22,29,111,50,0,0,0,0,0,1,0,110 8-Apr-22,50,98,63,0,0,0,0,0,0,0,110 9-Apr-22,80,95,102,1,0,0,0,0,0,1,110 10-Apr-22,46,101,67,0,1,0,0,0,0,0,110 11-Apr-22,41,114,75,0,0,1,0,0,0,0,110 12-Apr-22,15,114,31,0,0,0,1,0,0,0,110 13-Apr-22,31,96,38,0,0,0,0,1,0,0,110 14-Apr-22,54,105,83,0,0,0,0,0,1,1,110 15-Apr-22,35,110,56,0,0,0,0,0,0,0,110 16-Apr-22,61,96,76,1,0,0,0,0,0,0,110 17-Apr-22,78,96,98,0,1,0,0,0,0,1,110 18-Apr-22,31,115,50,0,0,1,0,0,0,0,110 19-Apr-22,18,112,23,0,0,0,1,0,0,0,110 20-Apr-22,46,100,63,0,0,0,0,1,0,0,110 21-Apr-22,20,110,32,0,0,0,0,0,1,0,110 22-Apr-22,52,95,64,0,0,0,0,0,0,0,110 23-Apr-22,67,95,84,1,0,0,0,0,0,0,110 24-Apr-22,37,113,72,0,1,0,0,0,0,0,110 25-Apr-22,60,95,79,0,0,1,0,0,0,1,110 26-Apr-22,74,101,100,0,0,0,1,0,0,1,110 27-Apr-22,32,98,35,0,0,0,0,1,0,0,110 28-Apr-22,41,103,60,0,0,0,0,0,1,0,110 29-Apr-22,44,96,55,0,0,0,0,0,0,0,110 30-Apr-22,49,111,89,1,0,0,0,0,0,0,110 1-May-22,51,100,70,0,1,0,0,0,0,0,110 2-May-22,35,111,60,0,0,1,0,0,0,0,110 3-May-22,54,97,72,0,0,0,1,0,0,1,110 4-May-22,28,100,36,0,0,0,0,1,0,0,110 5-May-22,43,98,59,0,0,0,0,0,1,0,110 6-May-22,54,112,96,0,0,0,0,0,0,1,110 7-May-22,47,101,66,1,0,0,0,0,0,0,110 8-May-22,62,98,85,0,1,0,0,0,0,0,110 9-May-22,36,103,54,0,0,1,0,0,0,0,110 10-May-22,46,95,59,0,0,0,1,0,0,0,110 11-May-22,32,111,58,0,0,0,0,1,0,0,110 12-May-22,57,103,82,0,0,0,0,0,1,1,110 13-May-22,37,100,51,0,0,0,0,0,0,0,110 14-May-22,60,108,100,1,0,0,0,0,0,1,110 15-May-22,45,109,76,0,1,0,0,0,0,0,110 16-May-22,51,105,77,0,0,1,0,0,0,0,110 17-May-22,33,113,64,0,0,0,1,0,0,0,110 18-May-22,27,113,59,0,0,0,0,1,0,0,110 19-May-22,24,114,39,0,0,0,0,0,1,0,110 20-May-22,43,104,62,0,0,0,0,0,0,0,110 21-May-22,79,97,99,1,0,0,0,0,0,0,110 22-May-22,56,95,73,0,1,0,0,0,0,0,110 23-May-22,40,95,48,0,0,1,0,0,0,0,110 24-May-22,52,96,62,0,0,0,1,0,0,0,110 25-May-22,61,96,77,0,0,0,0,1,0,1,110 26-May-22,24,114,45,0,0,0,0,0,1,0,110 27-May-22,35,109,57,0,0,0,0,0,0,0,110 28-May-22,56,105,80,1,0,0,0,0,0,0,110 29-May-22,62,97,80,0,1,0,0,0,0,0,110 30-May-22,73,101,105,0,0,1,0,0,0,1,110 31-May-22,27,110,48,0,0,0,1,0,0,0,110

3. Using the weeks of the day and the competitor's price and rain status in the data set as predictors, estimate the potential demand using linear regression. Report on the regression results (the quality of the fit, the significance of the predictors, overfitting etc.) and report the Root Mean Squared Error and Mean Absolute Percentage error for potential demand predictions in the training set and the test set. 4. Combine your best performing conversion rate estimator with the above potential demand estimator to find an estimator for the sales: d^(pj)=D^jd^(pj). Report the Root Mean Squared Error and Mean Absolute Percentage error for demand predictions in the training set and the test set. 5. Using your three models from Question 1. Find the optimal price (p) and the corresponding demand (d(p)), profit (m(p)=(pc)d(p)) and revenue ((r(p)=pd(p))) for each model. Take as incremental cost: c=0,10,20,30. Table 1: Sample result table for a given incremental cost Fill in four tables in the above format corresponding to c=0,c=10, and c= 20. Note that you can compute linear and exponential demand cases using calculus (as in the lectures). For logit demand (or any other complicated function) you can perform a numerical calculation by exhaustive discrete search (taking a grid between some pmin and pmax and start incrementing the price by small increments starting from pmin until pmax and recording the profit for each case). 3. Using the weeks of the day and the competitor's price and rain status in the data set as predictors, estimate the potential demand using linear regression. Report on the regression results (the quality of the fit, the significance of the predictors, overfitting etc.) and report the Root Mean Squared Error and Mean Absolute Percentage error for potential demand predictions in the training set and the test set. 4. Combine your best performing conversion rate estimator with the above potential demand estimator to find an estimator for the sales: d^(pj)=D^jd^(pj). Report the Root Mean Squared Error and Mean Absolute Percentage error for demand predictions in the training set and the test set. 5. Using your three models from Question 1. Find the optimal price (p) and the corresponding demand (d(p)), profit (m(p)=(pc)d(p)) and revenue ((r(p)=pd(p))) for each model. Take as incremental cost: c=0,10,20,30. Table 1: Sample result table for a given incremental cost Fill in four tables in the above format corresponding to c=0,c=10, and c= 20. Note that you can compute linear and exponential demand cases using calculus (as in the lectures). For logit demand (or any other complicated function) you can perform a numerical calculation by exhaustive discrete search (taking a grid between some pmin and pmax and start incrementing the price by small increments starting from pmin until pmax and recording the profit for each case)