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[answered] A large sports supplier has many stores located world wide.


A large sports supplier has many stores located world wide. A regression model is to be constructed to predict the annual revenue of a particular store based upon the population of the city or town where the store is located, the annual expenditure on promotion for the store and the distance of the store to the center of the city.

Data has been collected on 30 randomly selected stores:?show data

a)Find the multiple regression equation using all three explanatory variables. Assume that X1?is population, X2?is annual promotional expenditure and X3?is distance to city center. Give your answers to 3 decimal places.

y^?=??+?population +?promo. expenditure +?dist. to city

b)At a level of significance of 0.05, the result of the F test for this model is that the null hypothesis

isis not

rejected.

For parts?c)?and?d), using the data, separately calculate the correlations between the response variable and each of the three explanatory variables.

c)The explanatory variable that is most correlated with annual revenue is:

population
promotional expenditure
distance to city

d)The explanatory variable that is least correlated with annual revenue is:

population
promotional expenditure
distance to city

e)The value of R2?for this model, to 2 decimal places, is equal to?

f)The value of se?for this model, to 3 decimal places, is equal to?

g)Construct a new multiple regression model by removing the variable?distance to city center. Give your answers to 3 decimal places.

The new regression model equation is:

y^?=??+?population +?promo. expenditure

h)In the new model compared to the previous one, the value of R2?(to 2 decimal places) is:

increased
decreased
unchanged

i)In the new model compared to the previous one, the value of se?(to 3 decimal places) is:

increased
decreased
unchanged


 


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