Question

An economist with a major bank wants to learn, quantitatively, how much spending on luxury goods and services can be explained based on consumers’ perception about the current state of the economy and what do they expect in the near future (6 months ahead).  Consumers, of all income and wealth classes, were surveyed.  Every year, 1500 consumers were interviewed.  The bank having all of the data from the 1500 consumers interviewed every year, computed the average level of consumer confidence (an index ranging from 0 to 100, 100 being absolutely optimistic) and computed the average dollar amount spent on luxuries annually.  Below is the data shown for the last 24 years.

Date                 X                     Y (in thousands of dollars)

1994                79.1                 55.6

1995                79                    54.8

1996                80.2                 55.4

1997                80.5                 55.9

1998                81.2                 56.4

1999                80.8                 57.3

2000                81.2                 57

2001                80.7                 57.5

2002                80.3                 56.9

2003                79.4                 55.8

2004                78.6                 56.1

2005                78.3                 55.7

2006                78.3                 55.7

2007                77.8                 55

2008                77.7                 54.4

2009                77.6                 54

2010                77.6                 56

2011                78.5                 56.7

2012                78.3                 56.3

2013                78.5                 57.2

2014                78.9                 57.8

2015                79.8                 58.7

2016                80.4                 59.3

2017                80.7                 59.9

Question:

1. Explain how you would interpret the slope and the intercept of the regression model.

Answer 1

Here

X = Independent Variable = Consumer Confidence (Index ranging from 0 to 100)

Y = Amount spent on luxuries (in thousands of dollars)

(a) Interpretation of Slope:

Slope = m of the Regression Line implies that the amount spent on luxuries increases by m X1000 dollars for every increase of 1 unit in Consumer Confidence.

(b) Interpretation of the Intercept:

Intercept = b of the Regression Line implies that the amount spent on luxuries = b X 1000 dollars when the value of the Consumer Confidence = 0.