A Collection of Paired Data Consists of the Number of Years

question 52

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. The regression equation is
$$\text { Score } = 31.55 + 10.90 \text { Years }$$
$$\begin{array} { c c c c c c } \text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000 \\\mathrm {~S} = 5.651 \quad \mathrm { R } - \mathrm { Sq } = 83.0 \% & \mathrm { R } - \mathrm { Sq } & \text { (Adj) } = 82.7 \%\end{array}$$
Predicted values
$$\begin{array} { l l c c } \text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\53.35 & 3.168 & ( 42.72,63.98 ) & ( 31.61,75.09 ) \end{array}$$ What percentage of the total variation in test scores can be explained by the linear relationship between years of study and test scores?

• A)82.7%
• B)17.0%
• C)91.1%
• D)83.0%

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Definitions:

Point Elasticity

The measure of how much the quantity demanded of a good responds to a change in price at a specific point on the demand curve.

Producer Surplus

The difference between the amount a producer is paid for a good and the minimum amount they are willing to accept for producing it.

Equilibrium Quantity

The quantity of goods or services supplied is equal to the quantity demanded at the market price.

Equilibrium Price

The price at which the quantity demanded by consumers equals the quantity supplied by producers, resulting in market stability.