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%

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Definitions:

Overconfidence Effect

The cognitive bias where an individual's subjective confidence in their judgments is greater than their objective accuracy.

Availability Heuristic

A cognitive shortcut based on the first examples that surface in one's thoughts when considering a particular topic, idea, strategy, or choice.

Confirmation Bias

The tendency to interpret new evidence as confirmation of one's existing beliefs or theories.

Multitasking

The performance of multiple tasks simultaneously by an individual or machine.