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:
Point,Annual revenue,Population,Promo expenditure,Distance to city,
1,396,655,45,2,
2,220,304,80,16,
3,148,214,140,16,
4,621,940,113,11,
5,599,780,166,15,
6,155,115,95,10,
7,286,386,193,13,
8,552,682,169,19,
9,375,634,85,2,
10,184,207,86,7,
11,462,802,31,3,
12,288,389,174,6,
13,44,85,54,4,
14,268,389,147,7,
15,583,887,115,16,
16,223,269,119,3,
17,336,574,83,7,
18,524,690,133,17,
19,288,441,39,2,
20,510,642,138,3,
21,372,557,41,15,
22,572,957,80,13,
23,621,875,88,11,
24,607,748,187,8,
25,506,880,61,10,
26,490,649,110,3,
27,352,562,95,2,
28,36,56,87,7,
29,32,29,65,19,
30,606,865,72,5
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.
c)The explanatory variable that is most correlated with annual revenue is: (choose one)
population
promotional expenditure
distance to city
d)The explanatory variable that is least correlated with annual revenue is:(choose one)
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 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: (choose one)
increased
decreased
unchanged
i)In the new model compared to the previous one, the value of s (to 3 decimal places) is: (choose one)
increased
decreased
unchanged
