A group of researchers conducted a study to determine whether the final grade in an honors section of introductory psychology was related to a student’s performance on a test of math ability administered for college entrance. The researchers looked at the test scores of 200 students (n= 200) and found a correlation of r= .45 between math ability scores and final course grade. The proportion of the variability seen in final grade performance that can be predicted by math ability scores is .

And for this case

The % of variation is given by the determination coefficient given by and on this case , so then the % of variation explained is 20.25%.

The proportion of the variability seen in final grade performance that can be predicted by math ability scores is 20.25%.

Step-by-step explanation:

For this case we asume that we fit a linear model:

Where y represent the final grade and x the math ability scores

Where:  

And we can find the intercept using this:  

The correlation coeffcient is given by:

And for this case

The % of variation is given by the determination coefficient given by and on this case , so then the % of variation explained is 20.25%.

The proportion of the variability seen in final grade performance that can be predicted by math ability scores is 20.25%.

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step-by-step explanation:

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