The Spar in Muscat mall have recently introduced scanners at the checkout counters. The scanners record data on various aspects of a product, for instance, price, number of units sold and whether any...

The Spar in Muscat mall have recently introduced scanners at the checkout counters. The scanners record data on various aspects of a product, for instance, price, number of units sold and whether any promotional activities was carried out for that product or not. In doing so, the Spar management can evaluate whether price and promotional activities (if any) have any effect on sales of a product. Promotional activities are mainly of two types viz

• flyers distributed outside the store (Flyer) and


• (ii) in-store displays at the end of an isle that attract a customer’s attention to the said product (Display).

Data was collected on 40 different brand of food & beverage products for the month of May 2019, including sales(Y, number of units sold), price (X1, in OMR), flyer (X2, 1 if product was promoted through flyers, 0 if not) and display (X3, 1 if a special display of the product was used, 0 if not). As a preliminary analysis, a simple linear regression model was fitted to check the effect of price on sales. Part of the R output is given below:

RSquare = 59.7%.

1. Express the corresponding least squares regression model.


2. Interpret the slope coefficient


3. Suppose Hyper City is launching a new beverage brand which is priced at OMR136. What will be the predicted sale?


4. The proportion of variability in sales that is not accounted for by price is……


5. True/False : The correlation coefficient between price and sale is 0.773


6. Test whether sales have a significant linear association with price at 1% significance level.
   
   
   
   1. H0: Ha:
   
   
   2. Test statistic : t= (-0.014-0) / 0.0056 = -2.5
   
   
   3. Based on the p-value (0.0198) obtained, what will you conclude in the context of the problem?
   
   
   4. Now, the predictors flyer and display were added to the dataset and a multiple linear regression model was fitted. Part of the R output is shown below
   
   
   
   


7. 
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   
   

   	Estimate	Standard Error
   Intercept	81.23	35.24
   Price	-0.0318	0.023
   Flyer	10.21	3.28
   Display	21.67	13.27

   
   

   Adj R Square = 78.8%

   
   

1. Express the least squares regression model.


2. Interpret the coefficient of Flyer and Display in the context of the problem.

• 3-Calculate a 95% confidence interval of Flyer and interpret the same in the context of the problem. Can we say that promoting a product through fliers significantly affect its sales?


• 4-What is the coefficient of multiple determination of this model? Interpret its value.


• 5-Suppose you want to test whether Price has a
  positive
  effect on Sales controlling for Flyer and Display. Carry out an appropriate test at α = .05 and state your conclusion in the context of the problem.

Hypotheses : H0 :                               Ha :

t=-.0318-0/.023=-1.30

Test statistic :

Degrees of freedom :

Based on the p-value, you would

• Reject H0 at α = 0.01 but not at α = 0.05.


• Reject H0 at α = 0.05 and α = 0.01 but not at α = 0.1.


• Reject H0 at α = 0.05 and α = 0.1 but not at α = 0.01. Reject H0 at α = 0.1 but not at α = 0.01 and α = 0.05.


• Fail to reject H0 at all the above α values.


• Reject H0 at all the above α values.

1. Conclusion (in context of the problem)