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.
Score= 31.55+10.9 yrs
predictor coef stdev t p
constant 31.55 6.360 4.96 0.0
years 10.90 1.744 6.25 0.0

s= 5.651 R-sq= 83% R-sq(Adj)= 82.7%

perdict values fit 53.35 stdevfit = 3.168 95%CI=(42.72, 63.98) 95%PI ( 31.61, 75.09)

Use the software results above to determine what percentage of the total variation in test scores can be explained by the linear relationship between years of study and test scores?