A Collection of Paired Data Consists of the Number of Years

question 96

Multiple Choice

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting test score. $$\begin{array}{l}\text { The regression equation is }\\\begin{array} { l } \text { Score } = 31.55 + 10.90 \text { Years. } \\\begin{array} { l c c c c } \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000 \\\mathrm {~S} = 5.651 & \mathrm { R } - \mathrm { Sq } = 83.0 \% & \mathrm { R } - \mathrm { Sq } ( \mathrm { Adj } ) = 82.7 \% \\\text { Predicted values } \\\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\53.35 & 3.168 & ( 42.72,63.98 ) & ( 31.61,75.09 ) \end{array}\end{array}\end{array}$$ What percentage of the total variation in test scores is unexplained by the linear relationship between years of study and test scores?

• A)82.7%
• B)83.0%
• C)17.0%
• D)8.9%

---

Definitions:

Disabled

Individuals having a physical or mental condition that significantly limits their movements, senses, or activities.

Labor Earnings

Income received by workers for their labor or services, typically measured in terms of wages, salaries, or commissions.

Negative Income Tax

A system of social welfare that provides income to individuals or families below a certain income level, effectively supplementing their income.

Medicaid

A government-sponsored insurance program in the United States providing health care coverage to low-income individuals and families.