Use the Computer Display to Answer the Question $\text { Score }=31.55+10.90 \text { Years. }$

question 152

Multiple Choice

Use the computer display to answer the question.
-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.
The regression equation is $\text { Score }=31.55+10.90 \text { Years. }$

$\begin{array}{lcccc}\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000\end{array}$


$\mathrm{S}=5.651 \quad \mathrm{R}-\mathrm{Sq}=83.0 \% \quad \mathrm{R}-\mathrm{Sq}(\mathrm{Adj}) =82.7 \%$

$\text { Predicted values }$


What percentage of the total variation in test scores is unexplained by the linear relationship between years of
Study and test scores?

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

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Definitions:

Hypothesis

A specific prediction that can be tested, and proved or disproved.

Refuting

The act of disproving a statement or argument by presenting evidence or logical reasoning.

Empirical Evidence

Refers to the information obtained through observation and documentation of patterns and behaviors rather than theories or beliefs.

Observation

The act of closely monitoring or noting phenomena as they occur naturally without interfering or manipulating the situation.