Social Statistics by Thomas J. Linneman

Author:Thomas J. Linneman
Language: eng
Format: epub
Publisher: Routledge

We’ll interpret each piece step by step. First, the constant. It may seem odd that the constant is so very negative. How can one have such a negative income? Sometimes, the constant will seem quite odd because having the independent variable’s value be zero is quite odd in and of itself. This –132.45 means that if someone is zero inches tall, not only do they have to deal with all the horrible things that go along with that (just try finding clothes that fit!), but the regression equation predicts that they will have an income of –$132,450. Of course it makes no sense to be zero inches tall, and this is why the constant doesn’t make any sense.

Next, the slope. A vague interpretation is: as height goes up, income goes up. But we want to be as specific as possible: for every inch that height goes up, income goes up $2,660. Another way to get a feel for this effect is to plug in some hypothetical people. I ran a frequency distribution of the height variable, and found that the shortest person was 57 inches (or 4 feet 9 inches), the mean and median were 67 inches, and the tallest person was 79 inches (or 6 feet 7 inches). Here are predicted incomes for these three heights:

INCOME = –132.45 + 2.66 (57) = 19.17, or $19,700

INCOME = –132.45 + 2.66 (67) = 45.77, or $45,770

INCOME = –132.45 + 2.66 (79) = 77.69, or $77,690

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