To study fairness of IRS audits in a recent year,

To study fairness of IRS audits in a recent year, a researcher recorded for 20 US cities the percentage of individual or joint taxpayers audited along with the city's median household Income (in $1000). A scatterplot of the data with the least squares regression line is shown below. Below that are some basic descriptive statistics for the variables. Questions 3 - 6 concern this data and this regression. Along with noting the correct answer choice, briefly explain all answers.?

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Descriptive Statistics: Income ($1000), Audit%

Variable ? ? ? Count ? Mean ?StDev Minimum Maximum

Income ($1000) ? ?20 33.636 ?2.766 ?29.199 ?38.845

Audit% ? ? ? ? ? ?20 0.8300 0.2296 ?0.5000 ?1.3000

Correlation: Income ($1000), Audit%

Pearson correlation of Income ($1000) and Audit% = 0.466

Remember: For these questions, along with noting the correct answer choice, briefly explain all answers.

1. ? ? The equation of the least squares regression line to predict Audit% from Income ($1000) is:

A. ? -0.481 + 0.039(Income)

B. ? 0.481 + 0.039(Income)

C. ? 1.477 + 5.614(Income)

D. ? -1.477 + 5.614(Income)

Slope = r * (Sy / Sx) = 0.466 * (0.2296 / 2.766) = 0.039

Intercept = (mean of y) - 0.039*(mean of x) = 0.83 - 0.039*33.636 = -0.481

Thus, ANS is A

?

2. ? ? The percentage of variance in the Audit% variable explained by this regression with Income is approximately:

A. ? 21.7

B. ? 46.6

C. ? 0.466

D. ? 53.4

E. ? ?78.3

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3. ? ? If Income is recorded in dollars ($) instead of ($1000), the correlation between Audit% and Income ($) will be:

A. ? 0.0466

B. ? 0.466

C. ? 0.000466

D. ? 0.534

E. ? ?Cannot be determined without the raw data.

?

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4. ? ? The city with the lowest median income in this dataset is Jackson, MS. Its residual in this model is approximately:

A. ? 0.05

B. ? -0.05

C. ? -0.30

D. ? -0.20

E. ? ?-0.10


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