Question

# Each month, the owner of a restaurant records y=monthly sales receipts and x=amount spent that month...

Each month, the owner of a restaurant records y=monthly sales receipts and x=amount spent that month on advertising, both in thousands of dollars. For the first four months of operation, the observations are as shown in the table.
0 4
1 7
3 9
5 11
a.Find the mean and standard deviation for each variable.
b.Find the values for a and b in the regression line.
c. Find the correlation coefficient. Interpret the relationship between two variables using correlation coefficient.

 n= 4 X̅=ΣX/n 2.25 Y̅=ΣY/n 7.75 sx=(√(Σx2-(Σx)2/n)/(n-1))= 2.2174 sy=(√(Σy2-(Σy)2/n)/(n-1))= 2.9861 Cov=sxy=(ΣXY-(ΣXΣY)/n)/(n-1)= 6.4167 r=Cov/(Sx*Sy)= 0.9691

a)

mean of Sales =7.75

standard deviation of Sales =2.9861

b)

 slope= b  = r*Sy/Sx=1.3051 intercept= a     = (Σy-β1Σx)/n=4.8136

c)

correlation coefficient r=0.9691

since correlation coefficient is positive and near 1 , there apears a strong positive linear relation between advertisement and sales

#### Earn Coins

Coins can be redeemed for fabulous gifts.