Question

#4

The numbers in the table below represent the average daily intake of sugar-sweetened soft drinks and the average weight for a particular group of men at various times over a period of 40 years. Use that data to answer the questions below.

Soda intake (gal)	8	13	18	22	21	27	24	31	31	32	41	44	38
Weight (lb)	173	169	167	169	176	167	184	183	172	172	182	181	192

To two decimal places, the correlation coefficient is

To the nearest integer percent, about what percentage of weight gain is explained by soft drink consumption?  %

To four decimal places, the coefficients of the regression line are:

slope:         intercept:

Answer 1

X Values
∑ = 350
Mean = 26.923
∑(X - M_x)² = SS_x = 1370.923

Y Values
∑ = 2287
Mean = 175.923
∑(Y - M_y)² = SS_y = 730.923

X and Y Combined
N = 13
∑(X - M_x)(Y - M_y) = 583.923

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

r = 583.923 / √((1370.923)(730.923)) = 0.58

So r^2=0.58^2=0.34

So 34% of weight gain is explained by soft drink consumption.

Sum of X = 350
Sum of Y = 2287
Mean X = 26.9231
Mean Y = 175.9231
Sum of squares (SS_X) = 1370.9231
Sum of products (SP) = 583.9231

Regression Equation = ŷ = bX + a

b = SP/SS_X = 583.92/1370.92 = 0.4259

a = M_Y - bM_X = 175.92 - (0.43*26.92) = 164.4556

ŷ = 0.4259X + 164.4556

Slope: 0.4259

Intercept: 164.4556