Exercises in Interpretation

Suppose we estimated the determinants of monthly expenditures on ice cream. The dependent variable, y, is ice cream expenditures (in dollars and cents), in a given month for a sample of families in Los Angeles. The independent variables are X₁, monthly family income (in dollars and cents) and X₂=1 if the family lives in West Los Angeles, =0 otherwise. The standard errors of the parameter estimates are in parentheses.

=-25.54 + 0.05X₁ + 0.06X₂

(10.25) (0.20) (0.015) df=100 R²=.25

Which interpretations of b₂ are valid?

A. Holding income constant, West LA families spend significantly more on ice cream per month than non-West LA families.

B. The statistically significant result suggests a West LA family buys more ice cream than a non-West LA family with the same income.

C. West LA families spend on average six cents more on ice cream than non-West LA families per month; this relationship is statistically significant.

D. While statistically significant, the difference in predicted ice cream expenditures between West LA and non-West LA families is quite small, only six cents a month.

=-25.54 + 0.05X₁ + 0.06X₂

(10.25) (0.20) (0.015) df=100 R²=.25

Which interpretations of b₁ are valid?

A. The smaller coefficient for the income variable indicates that a family’s income has a smaller effect on ice cream expenditure than the family’s location has.

B. Holding the location constant, family income has a large predicted effect on ice cream purchases; an extra $1000 in monthly income causes predicted expenditures to increase by $50 per month.

C. The effect family income is estimated to have on ice cream expenditure is not statistically significant.

D. The income effect on ice cream expenditures, while large, is imprecisely estimated.

Suppose we want to estimate the determinants of the size of single family homes recently built in the LA area. You run the regression on a sample of houses:

= b₀ + b₁X₁ + b₂X₂ + b₃X₃

where the dependent variable, y, is the square footage of the house, X₁ is the average price of an acre of land in the zip code the house is in, X₂ is median household income of the zip code and X₃ is house size in square meters.

What is wrong with this model? Can we determine without estimating the model what b₃ equals? What would R² equal?

Suppose we ran, for a sample of households, the regression: where x is monthly household income (in dollars and cents) and y is monthly consumption of food (in calories).

A. Explain why b₀ will likely be greater than zero.

B. Explain why this is a correct statement: If, within the equation, b₁ =0 then R² equals 0.

C. Explain why b₁ is unlikely to equal 0.

D. Explain why b₁ is unlikely to be less than zero.

Examples on Conveying Ideas in Narrative

Describing magnitudes of data:

A. In 2001, the average temperature in the New York City area was 56.3 degrees Fahrenheit.

B. In 2001, the average temperature in the New York City area was 56.3 degrees Fahrenheit, 1.5 degrees above normal.

C. In 2001, the average temperature in the New York City area was 56.3 degrees Fahrenheit, 1.5 degrees above normal, making it the seventh warmest year on record for the area.

Describing magnitudes of data:

A. In 1998, total expenditures on health care in the United States were estimated to be more the $1.1 trillion (Centers for Medicare and Medicaid Services 2004).

B. In 1998, total expenditures on health care in the United States were estimated to be more the $1.1 trillion, equivalent to $4,178 for every man, woman and child in the nation (Centers for Medicare and Medicaid Services 2004).

C. In the US, per capita health expenditures averaged $4,108 in the 1990’s, equivalent to 13% of GDP – a higher share of GDP than in any other country in the sample period. In comparison, Switzerland – the country with the second highest per capita health expenditures – spent approximately $3,835 per person, or 10.4% of GDP. No other country exceeded $3,000 per capita on health expenditures (World Bank 2001b).

Causality and Active Voice:

A. The new math curriculum is expected to be associated with higher math scores.

B. We expect that the new math curriculum will be associated with higher math scores.

C. We expect that adoption of the new mathematics curriculum will improve math scores.

Definition:

A. In 1996, the voter turnout for the presidential election was 63%.

B. In 1996, 63% of the 146 million registered voters participated in the US presidential election.

C. In 1996, 63% of the 146 million registered voters participated in the US presidential election. As a percentage of the voting age population (197 million people), however, voter turnout was only 47%, revealing a large pool of potential voters who did not participate.