## Answers

**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*= 1008571.43/4994285.71 = 0.2020

_{X}*a*= M

_{Y}-

*b*M

_{X}= 657.14 - (0.2*2328.57) = 186.8993

ŷ = 0.2020

*X*+ 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**.