A Collection of Paired Data Consists of the Number of Years

question 29

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. $$\text { The regression equation is }$$
$\begin{array}{l}\text { Score }=31.55+10.90 \text { Years. }\\\begin{array}{lllcc}\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000\end{array}\end{array}$
$$S=5.651 \quad R-S q=83.0 \% \quad R-S q(\text { Adj }) =82.7 \%$$
Predicted values
$\begin{array}{llcc}\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\ 53.35 & 3.168 & (42.72,63.98) & (31.61,75.09) \end{array}$ If a person studies 4.5 years, what is the single value that is the best predicted test score? Assume that there is a significant linear correlation between years of study and test score.

• A)53.35
• B)80.6
• C)83.0
• D)49.1

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Definitions:

Displacement

In physics, the movement of an object from one position to another or the volume displaced by an object in a fluid.

Business Conditions

Describes the state of the economy and market environment in which a business operates, affecting its performance and strategy.

Defense Mechanism

Psychological strategies unconsciously used to protect a person from anxiety arising from unacceptable thoughts or feelings.

Regression

A statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables.