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

Questions:

1. Measure the strength of the linear association between consumers’ moods and the dollar amounts spent on luxury items.
2. Construct the linear regression model for the dollar amount spent on luxury goods and services.
3. Explain how you would interpret the slope and the intercept of the regression model.
4. How well does our model fit the data? Explain what it means.
5. Do you think that measuring the level of optimism is a good predictor for trying to forecast future spending on luxury items?  Explain why or why not.
6. How would you be able to improve on the model?  You must provide a minimum of two specific ways to go about improving the model.
7. If the economist expects that, by year’s end, the average level of consumer confidence will hit 81.5 points, how much will be expected by consumers to spend on luxury items?

Answer 1

i. The Correlation Coefficient between X and Y-0.5701 ii. Linear regression equation: Y 2.05350.6862X ii. Interpretation of slope: If we increase average level of consumer confidence by one unit then the average dollar amount spent on luxuries annually is increased by 686.2 Interpretation of intercept: When average level of consumer confidence is zero then the average dollar amount spent on luxuries an- nually is $ 2053.5. iv. R2-0.3250 i.e. 32.50% of total variation of the average dollar amount spent on luxuries annually is explained by average level of consumer confidence by this regression line.

SUMMARY OUTPUT 79.1 79 80.2 80.5 81.2 80.8 81.2 54.8 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.570118553 0.325035165 0.294354945 1.224914752 24 55.9 57.3 57.5 56.9 55.8 56.1 ANOVA 80.3 Significance F 79 MS Regression Residual Total 1 15.89584473 15.89584 10.59429 0.003629948 78.3 78.3 77.8 22 33.00915527 1.500416 48.905 23 Coefficients Standard Error t Stat P-value Lower 95% 2.053547272 16.72178923 0.122807 0.903375 -32.62532105 36.7324156 0.686200938 0.2108217273.254887 0.00363 0.248983437 1.123418439 Upper 95% Intercept X Variable 1 78.5 78.3 78.5 78.9 79.8 56.3 57 57.8 58 59.3 59.9