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%.

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w