The following data represent Aggregate Consumption (Y) and Disposable Income (X) for one country.
Year Y X
1993 103 114
1994 105 118
1995 108 126
1996 107 130
1997 122 136
1998 124 140
1999 128 148
2000 130 156
2001 142 160
2002 147 164
2003 154 170
2004 151 178
a. Draw a scatter diagram for the data in the table above. Determine by inspection if there exists an approximate linear relationship between Y and for the years from 1993 to 2004.
b. State the general form of the linear regression equation between consumption, Y, and disposable income, X. Why would you expect that most observed values of Y do not fall exactly on the straight regression line?
c. What is meant by the least squares principle of estimating the "best" straight line that fits the sample of XY observations? Why do we not simply take the sum of the vertical deviations without squaring them? Why do we not take the sum of the absolute deviations?
d. Find the values for the y-intercept and the slope of the regression line. Plot the regression line on a graph and show the deviations of each Y from the corresponding estimated consumption level (Y').
e. Calculate the "standard error of the estimate".
f. Calculate the SSE (Error variation), SS Total (Total variation), SSR (Variation explained by the regression), the correlation coefficient and the coefficient of determination. How would you interpret each of these quantities?
Step by step method for regression analysis is discussed here. Regression coefficients, coefficient of determination, scatter diagram and significance of regression model are explained in the solution.