Question

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

Annual revenue ($) (× 1000)	Population (× 1000)	Annual promotional expenditure ($) (× 100)	Distance to city center (mi)
859	808	133	5
648	689	85	3
192	120	102	15
689	722	80	13
755	752	161	12
334	292	92	7
553	535	121	3
587	611	43	18
807	768	79	1
556	600	96	16
601	451	199	9
529	422	186	11
941	942	75	5
609	526	111	19
353	234	140	19
950	924	195	3
72	21	93	18
883	870	56	5
853	846	147	18
286	263	75	5
269	251	34	19
777	781	95	5
786	851	34	19
115	120	107	1
644	659	37	3
423	312	179	2
457	408	72	6
819	873	52	19
717	664	121	7
554	622	69	1

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

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 s_e 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 s_e (to 3 decimal places) is:

increased
decreased
unchanged

Answer 1

A)The multiple regression model is

y^= -5.176 + .912 population + .729promo.expenditure + .302dist to city

B)Since p value is less than .05 in the ANOVA table , we reject the null hypothesis and conclude that the model with independent variables is significant than the intercept only model

C)The explanatory variable that is most correlated with the annual revenue is population (.98)

D)The explanatory variable that is least correlated with the annual revenue is promo.expenditure (.056)

E)R² = 0.98

F)SE = 36.693

G)The new regression model with distance to city center removed is

y^ =-.983 +.911 population +.723promo.expenditure

H)R² = .98; compared to the first model the value has unchanged

I)SE = 36.067;compared to the first model the value has decreased