Question

Wendy's wonders how to price its new chili salad. It test-markets five different prices in the cities listed below, with the listed resultant sales (in thousands of dollars). Manually calculate correlation, and the regression model. Show your work.

City	Sales($000s)	Price($)	Price^2	Sales^2	Price*Sales
Rochester	75	0.99	0.98	5625.00	74.3
Ottumwa	70	1.29	1.66	4900.00	90.3
Seattle	45	1.49	2.22	2025.00	67.1
Raleigh	33	1.89	3.57	1089.00	62.4
Denair	42	2.19	4.80	1764.00	92.0
sum	265	7.85	13.23	15403.00	386.0
mean	53	1.57	2.65	3080.60	77.2
st.dev.	18.4	0.5	1.53	2037.06	13.4

Answer 1

X Values
∑ = 265
Mean = 53
∑(X - M_x)² = SS_x = 1358

Y Values
∑ = 7.85
Mean = 1.57
∑(Y - M_y)² = SS_y = 0.908

X and Y Combined
N = 5
∑(X - M_x)(Y - M_y) = -30.1

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -30.1 / √((1358)(0.908)) = -0.8572

Sum of X = 265
Sum of Y = 7.85
Mean X = 53
Mean Y = 1.57
Sum of squares (SS_X) = 1358
Sum of products (SP) = -30.1

Regression Equation = ŷ = bX + a

b = SP/SS_X = -30.1/1358 = -0.0222

a = M_Y - bM_X = 1.57 - (-0.02*53) = 2.7447

ŷ = -0.0222X + 2.7447