Question

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. Calculate accountable, unaccountable, and total variation. Show your work.
2. 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.

Answer 1

	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

Please let me know in case of any doubt.

Thanks in advance!

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