Here are some real numbers -- unfortunately a little out of date, but they can illustrate the approach. Figure 1 shows a scatterplot of the personal disposable income and consumption of the population of the United States, for the years 1929-1982, in dollars of 1982 purchasing power.
Each x corresponds to the income (on the horizontal axis) and the consumption (on the vertical axis) for one of the years between 1929 and 1982 inclusive. As you can see, the points fit rather well a linear "consumption function" equation
C = 14.11 + .89 Y
where Y is interpreted as Personal Disposable Income (that is, income after taxes) and both consumption and income are measured in billions of dollars. This equation was estimated by a simple statistical method. But it is only an illustration, since many economists believe that the consumption function is actually somewhat too complicated to be estimated by very simple methods.