Question

Favors Distribution Company purchases small imported trinkets in bulk, packages them, and sells them to retail stores. The managers are conducting an inventory control study of all their items, and they have collected the following sales data for one such item over twelve (12) months. Suppose that someone has gotten started calculating the least-squares equation for the data, and hands you the table below.

What is b, the slope of the regression line?

∑xy 1,660

x-bar 6.5

y-bar 75

∑x(squared) 650

Answer 1

y= bx + c

where b is the slope of the regression equation and c is the constant.

Mean X = 6.5
Mean Y = 75
Sum of squares (SS_X) = 650
Sum of products (SP) = 1660

Regression Equation = ŷ = bX + c

b = SP/SS_X = 1600/650 = 2.4615

a = M_Y - bM_X = 75 - (2.4615*6.5) = 59

ŷ = 2.4615x + 59

So the value of b is 2.4615