Imagine that you have come across a magazine article reporting the following rel
ID: 452596 • Letter: I
Question
Imagine that you have come across a magazine article reporting the following relationship between annual expediture on prepared dinner (PD) and annual income (INC):
PD=23.4+0.003 INC
The coefficient of INC variable is reported as significant.
a. Does this relationship seem plausible? Is it possible to have a coefficient that is samll in magnitude and yet significant?
b. From the information given, can you tell how good the estimated model is?
c. What are the expected expenditures on PDs of a family earning $30,000?
d. If a family earning of $40,000 spent $130 annually on PDs, what is the residual?
e. What is the meaning of a negative residual?
Explanation / Answer
Yes, the relationship could be plausible. There’s supposed to be direct relationship between annual income and expenditure. Small coefficients could be significant, because coefficients are partial derivatives of Y with respect to X. and their significant actually depends on the magnitude of X and units of measurement. In this case, INC is supposed to be a relatively large number, so the overall impact of coefficient would be quite significant. The estimated model seems reasonably estimated. Expected expenditure on PDS = 23.4 + 0.003*30000 = 113.4 Residual = 130 - 23.4 + 0.003*40000 = - 13.4 Negative residual mean that data point is lying below the graph of regression equation.