Question

Managers of an outdoor coffee stand in Coast City are examing the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by
y, in dollars) and the maximum temperature (denoted by
x, in degrees Fahrenheit) for each of sixteen randomly selected days during the past year are given below. These data are plotted in the scatter plot in Figure 1.

Answer 1

a) Sum of X = 940.7
Sum of Y = 30026.2
Mean X = 58.7938
Mean Y = 1876.6375
Sum of squares (SS_X) = 3018.1294
Sum of products (SP) = -30030.5763

Regression Equation = ŷ = bX + a

a=Y intercept

a = M_Y - bM_X = 1876.64 - (-9.95*58.79) = 2461.64

b. For the given sample data in question correlation coeeficient is calculated as

X Values
∑ = 940.7
Mean = 58.794
∑(X - M_x)² = SS_x = 3018.129

Y Values
∑ = 30026.2
Mean = 1876.637
∑(Y - M_y)² = SS_y = 801192.238

X and Y Combined
N = 16
∑(X - M_x)(Y - M_y) = -30030.576

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

r = -30030.576 / √((3018.129)(801192.238)) = -0.611