SIMPLE LINEAR REGRESSION ANALYSIS

The Ordinary Least Squares Method

1. Assume a sample is taken of six households asking for the levels of income (X) and

consumption (Y) in thousands of dollars as reported in the following table:

X Y XY X2 Y2

25 23 575 625 529

30 28 840 900 784

35 31 1085 1225 961

40 36 1440 1600 1296

45 41 1845 2025 1681

50 46 2300 2500 2116

a. Draw a Scatter Diagram

b. Derive the equation for the least squares regression line which will best fit the data

c. Does the sign of the slope coefficient make economic sense? Interpret its meaning.

d. Determine Point Estimation

e. Determine the Standard Error

f. Determine the coefficient of correlation, coefficient of determination, and Adjusted r²

What do these coefficients tell you?

g. Do hypothesis testing using = 0.05

Please complete every single step. thank you.