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). Calculate correlation, and the regression model.

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
∑ = 601.4
Mean = 75.175
∑(X - M_x)² = SS_x = 43565.315

Y Values
∑ = 17.77
Mean = 2.221
∑(Y - M_y)² = SS_y = 38.098

X and Y Combined
N = 8
∑(X - M_x)(Y - M_y) = 1222.75

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

r = 1222.75 / √((43565.315)(38.098)) = 0.9491

Sum of X = 601.4
Sum of Y = 17.77
Mean X = 75.175
Mean Y = 2.2213
Sum of squares (SS_X) = 43565.315
Sum of products (SP) = 1222.7503

Regression Equation = ŷ = bX + a

b = SP/SS_X = 1222.75/43565.32 = 0.0281

a = M_Y - bM_X = 2.22 - (0.03*75.18) = 0.1113

ŷ = 0.0281X + 0.1113