Wendy’s is offering a new Wolfburger as a promotional tie-in for the new sequel in the...

Wendy’s is offering a new Wolfburger as a promotional tie-in for the new sequel in the Twilight motion picture series, and wonders how much they should charge. It test-markets five different prices in the cities listed below, with the listed resultant sales (in thousands of dollars):

City	Sales($000s)	Price($)	Price²	Sales²	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

a.) Compute (numerically) and interpret (in words) the correlation between sales and price
b. ) Estimate the regression function between sales and price

Expert Solution

a.

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

b.

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

orchestra answered 3 years ago

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