3. A sample of seven households was obtained, and information on their income and food expenditures for the past month

Solution:

Given that the following information

A sample of seven households was obtained, and information on their income and food expenditure for the past month was collected.

a.

b.

a.X Values
∑ = 16300
Mean = 2328.571
∑(X - M_x)² = SS_x = 4994285.714

Y Values
∑ = 4600
Mean = 657.143
∑(Y - M_y)² = SS_y = 237142.857

X and Y Combined
N = 7
∑(X - M_x)(Y - M_y) = 1008571.429

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

r = 1008571.429 / √((4994285.714)(237142.857)) = 0.9268

Hence there is strong positive correlation

b.

Sum of X = 16300
Sum of Y = 4600
Mean X = 2328.5714
Mean Y = 657.1429
Sum of squares (SS_X) = 4994285.7143
Sum of products (SP) = 1008571.4286

Regression Equation = ŷ = bX + a

b = SP/SS_X = 1008571.43/4994285.71 = 0.2020

a = M_Y - bM_X = 657.14 - (0.2*2328.57) = 186.8993

ŷ = 0.2020X + 186.8993

c. For every increase in x, y will change to 0.2020 and this is value of slope

d.

For x=5200,

ŷ = (0.2020*5200) + 186.8993=1237.2993

e.