A manager of a pizza outlet has collected monthly sales in 0

A manager of a pizza outlet has collected monthly sales (in $000) data for some time in an attempt to predict sales for the outlet. During this time, the outlet has been running a series of different advertisements. The manager has kept track of X1, the number of advertisements that have appeared as well as X2, the cost of these advertisements (in hundreds of dollars) for each month. The data are given. The initial model is Sales = Bo + B1*X1 + B2*X2 . Consider at least three different models, determine a \"best\" model for predicting Sales, and explain why each is or is not your \"best\".. Feel free to transform any of the variables and use them in your models. Use your \"best\" model to estimate Sales for May, 2014, if there are to be 10 ads purchased for a total cost of $1500. Month No. of Ads Cost of Ads Sales Jan-13 11 14 49.4 Feb-13 8 11.8 47.5 Mar-13 11 15.7 52.6 Apr-13 14 15.5 49.3 May-13 17 19.5 61.1 Jun-13 15 16.8 53.2 Jul-13 12 12.8 47.4 Aug-13 10 13.6 49.4 Sep-13 17 18.2 62 Oct-13 11 16 47.9 Nov-13 8 13 47.3 Dec-13 18 20 61.5 Jan-14 12 15.1 54.2 Feb-14 10 14.2 44.7 Mar-14 13 17.3 53.6 Apr-14 12 15.9 55.4 Can I get a clear answer to this question please.

Solution

Model 1) No of ads Vs Sales

The regression model is y=a+bx

where y is sales and x is No.of ads

From the Excel.

The fitted Regression model is y=33.34+1.52(No.of ads)

And R square value is 0.72 ie.,72% variation is due to the factor No.of ads

Model2)

Cost of ads Vs Sales

The regression model is y=a+bx

where y is sales and x is Cost of ads

From the Excel.

The fitted Regression model is y=21.02+2.01(cost .of ads)

And R square value is 0.75 ie.,75% variation is due to the factor No.of ads

Model3)

Cost of ads and No of ads Vs Sales

The regression model is y=a+bx1+cx2

where y is sales and x1 is Cost of ads and x2 is N.of ads

From the Excel.

The fitted regression equation is y=24.8231+0.66(No. of ads)+ 1.23(cost of ads)

The R sqaure value is 0.7789 ie., 78% variation is due to two factors (no.of ads, cost for ads).

Hence from above 3 models the best model is third model since Rsqaure value more than other two models