Question

In: Accounting

Suppose data were collected on the number of customers that frequented a grocery stores on randomly...

Suppose data were collected on the number of customers that frequented a grocery stores on randomly selected days before and after the governor of the state declared a lock down due to COVID 19. A sample of 6 days before the lockdown were chosen as well as 6 days randomly chosen after the lock down was in place. The number of shoppers each day were as follows:

Before lock down

After lock down

100

60

110

50

115

70

120

90

145

40

130

50

This is interval/ratio data because they are characteristics of the days.

  1. Can these results be generalized? To whom?
  2. Can cause and effect statements be made? Explain.
  3. Calculate accountable, unaccountable, and total variation. Show your work.
  4. Eta square is accountable variation divided by total variation. Determine eta square. It is interpreted as the variation in the dependent variable that can be accounted for by the independent variable. Describe eta square in terms of this problem.

Solutions

Expert Solution

ΣX ΣY Σ(x-x̅)² Σ(y-ȳ)² Σ(x-x̅)(y-ȳ)
total sum 720.00 360.00 1250.00 1600.00 -550.00
mean 120.00 60.00 SSxx SSyy SSxy

Sample size,   n =   6      
here, x̅ = Σx / n=   120.000          
ȳ = Σy/n =   60.000          
SSxx =    Σ(x-x̅)² =    1250.0000      
SSxy=   Σ(x-x̅)(y-ȳ) =   -550.0      
              
estimated slope , ß1 = SSxy/SSxx =   -550/1250=   -0.4400      
intercept,ß0 = y̅-ß1* x̄ =   60- (-0.44 )*120=   112.8000      
              
Regression line is, Ŷ=   112.800   + (   -0.440   )*x
              
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    1358.0000      
std error ,Se =    √(SSE/(n-2)) =    18.4255      
              

Anova table
variation SS
regression 242.00
error, 1358.00
total 1600.000

Eta square = 242.00/ 1600.000

= 0.1513

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