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A Collection of Paired Data Consists of the Number of Years

question 52

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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
 Score =31.55+10.90 Years \text { Score } = 31.55 + 10.90 \text { Years }
 Predictor  Coef  StDev  T  P  Constant 31.556.3604.960.000 Years 10.901.7446.250.000 S=5.651RSq=83.0%RSq (Adj)  =82.7%\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
 Fit  StDev Fit 95.0% CI 95.0% PI 53.353.168(42.72,63.98) (31.61,75.09) \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?

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Definitions:

Gross Method

An accounting practice where invoice transactions are recorded at their full, or gross, amounts before any discounts are applied.

Periodic Inventory Method

An accounting approach where inventory is physically counted at specific intervals to determine the cost of goods sold.

Merchandise Purchase

Refers to the acquisition of goods to be sold in the normal course of business.

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