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:

Higgins's Self-discrepancy Theory

A theory positing that individuals experience emotional discomfort or psychological distress due to discrepancies between their actual self, ideal self (aspirations), and ought self (sense of duty or obligation).

Ought Self

An individual's representation of what they believe they should be, often influenced by societal expectations.

Ought Self

A component of self-concept representing the attributes an individual or others believe they should possess.

Ideal Self

The version of oneself that a person aspires to be, encompassing their goals, values, and desires for personal improvement.