Dummy (indicator) variables in regression

Sales data for single-family houses in an Indianapolis suburb were used to estimate this equation in 2005:

where: Y = sale price $\mathrm{S}=$ square feet of living area G = garage square feet A = age of house in years B = number of baths $\mathrm{T}=1$ if it is two-story, 0 if not.

The standard errors are in parentheses.

Identify five errors in these reported results from a multiple regression model for predicting the number of home sales, using quarterly timeseries data from 2001 to 2020:

Identify five distinct problems with this multiple regression model of the effect of COVID-19 on the earnings of small business owners.

Earnings $=$ annual income from business, dollars COVID = 1 during COVID months, 0 pre-COVID Race $=0$ if white, 1 if black, 2 if Asian

A study of the income of family-law lawyers looked at the influence of age, sex, and law school attended:

where: $\mathrm{Y}=$ average income over the past 5 years X = current age $\mathrm{D}_{1}=0$ of male, 1 if female $\mathrm{D}_{2}=1$ if attended Harvard, 2 if attended Yale, 3 if attended Stanford, and 0 otherwise.

What is the most important problem with this model specification?

A study compared the daily returns for a portfolio of stocks that have clever ticker symbols to the performance of the overall market for the years 1984-2005. Part of the study involved the estimation of this regression equation,

[3.45] [39.52] where Y is the clever-ticker daily return, X is the stock market daily return, and the t -values are in brackets.

An update of this study using data for 2006-2018:

How could you test if the differences in the estimated coefficients (.00049 versus .00026 and .81 versus .88) are statistically persuasive? Be specific.

A study of the effect of birth order on GPA reported these results:

where: Y = GPA, scale of 0-4 X1 = height, in inches X2 = 1 if female, 0 otherwise X3 = 1 if only child, 0 otherwise

X4 = 1 if first born, 0 otherwise X5 = 1 if not an only child or first-born, 0 otherwise [ ] = absolute value of t -values Why do you suspect that this is not an honest report of the results?

In a 1980 court case, a federal judge described how regression estimates of male and female salary equations could be used to determine if an employer discriminates against females.

where: $\mathrm{Y}=$ annual earnings $\mathrm{S}=$ number of years of schooling $\mathrm{E}=$ number of years of relevant job experience The judge also noted that in place of two separate equations, one for males and one for females, the following single equation could be estimated, where $\mathrm{D}=0$ if the person is a male and $\mathrm{D}=1$ if the person is female:

Traffic fines for speeding in California are supposed to be determined by a formula based on how many miles over the speed limit the driver was driving, but there is flexibility in various extra fees. A researcher wants to see if total speeding fines are higher for people under the age of 30 than for older drivers.

A dean claims that humanities professors' salaries Y are determined solely by teaching experience X. To see if there is a statistically persuasive difference in the salaries of male and female humanities professors, the equation $Y=\alpha +\beta_{1} D+\beta_{2} X+\beta_{3} D X+\varepsilon$ was estimated, using the variable $D=0$ if male, 1 if female.

A researcher was interested in how a movie's box office revenue is affected by the audience suitability rating assigned by the Motion Picture Association of America (MPAA) and the quality of the film as gauged by Entertainment Weekly's survey of ten prominent film critics. Data for 105 films that were critically rated in 1991 were used to estimate the following equation by ordinary least squares:

[.61] [4.36] [3.74] where: $\mathrm{Y}=$ domestic box office revenue, in dollars $\mathrm{D}=$ MPAA suitability rating ($\mathrm{D}=0$ if rated G, PG, or PG-13; $\mathrm{D}=1$ if rated R) $\mathrm{X}=$ Entertainment Weekly quality rating $(12=\mathrm{A}, 11=\mathrm{A}-10=\mathrm{B}+, \ldots )$ [ ]: t-values Explain the errors in each of these three critiques:

Identify the most serious problem with this model of household income

where: $\mathrm{Y}=$ average household income in state $\mathrm{D}=$ state dummy variable; 1 for Alabama, 2 for Alaska, 3 for Arizona, etc. $\mathrm{E}=$ average education in state $\mathrm{A}=$ average age in state

This model was estimated by ordinary least squares using 2011 data for individuals:

where: $\mathrm{Y}=$ logarithm of income A = age E = education, years $\mathrm{F}=$ female; 1 if female, 0 if male $\mathrm{M}=$ married; 1 if married, 0 if unmarried $\mathrm{U}=$ unmarried; 0 if unmarried, 1 if married What statistical problem do you see?

This regression equation was estimated using data for 481 California Census blocks that were more than $95 \%$ Hispanic in 2008:

where: P = of the two-party vote received by Barack Obama in the 2008 Presidential election $\mathrm{Y}=$ median household income of Hispanics ($1000s of dollars) $\mathrm{D}=0$ if the Census block is in L.A. County; D = 1 otherwise and the t -values are in brackets. Explain why you either agree or disagree with these conclusions:

A random sample of 100 college students yielded data on $Y=$ student's height, $X_{1}=$ student's sex (0 if female, 1 if male), $X_{2}=$ mother's height, and $\mathrm{X}_{3}=$ father's height. All heights were measured in feet; for example, a 5 foot, 3 -inch person is 5.25 feet tall.

Interpret these regression results using quarterly data for 1974-2014. The dependent variable is housing starts, in thousands. The explanatory variables are: Time $=1$ in the first quarter of 1974, 2 in the second quarter of 1974, etc. Q2 = 1 in second quarter, 0 otherwise Q3 = 1 in third quarter, 0 otherwise Q4 = 1 in fourth quarter, 0 otherwise

A multiple regression equation was used to explain rents paid by people who live and work in Phoenix:

where: $\mathrm{Y}=$ monthly rent X = monthly income $\mathrm{D}=1$ if full-time job, 0 if part-time

Explain why you either agree or disagree with this interpretation of $\beta_{2}$ : "The coefficient of the dummy variable measures the extent to which renters can afford to pay a higher rent because their full-time job gives them more income."

A survey of 47 college sophomores investigated the effect of studying and extracurricular activities on grades:

where: $\mathrm{Y}=$ grade point average on a 12 -point scale $\mathrm{X}=$ average hours per week spent studying; $\mathrm{D}=1$ if the person spends at least 10 hours a week on an extracurricular activity such as work or sports, 0 otherwise and the standard errors are in parentheses. The researcher concluded that, "The effect of extracurricular activity is not significant and does not lend support to the commonly held notion that extracurricular activity negatively affects grades because it reduces available study time." Explain why the coefficient of D does not measure the extent to which extracurricular activity affects grades by reducing available study time.

A researcher specified this time-series model of consumer spending,

where: C = consumer spending $\mathrm{Y}=$ disposable income $\mathrm{D}=1$ if the stock market went up that year, 0 otherwise What errors do you see in these reported results?

What is the most important thing wrong with these multiple regression results that examined the relationship between year in college and mental depression?

Dependent variable: Depression = survey, measured on a scale of 0-10 Explanatory variables: Frosh = 1 if first year, 0 otherwise Sophomore $=1$ if second year, 0 otherwise Junior = 1 if third year, 0 otherwise Senior = 1 if fourth year or longer, 0 otherwise Results