The amygdala is a brain structure involved in the processing and memory of emotional reactions.In a research project,10subjectswere shown emotional video clips.They then had their brains scanned with positron emission tomography(PET),and their memory of the clips was assessed quantitatively.Here are the relative amygdala activity and the memory score for each subject:

Relation activity - 0.417 -0.258 -0.234 -0. 249 -0. 156

Memory score 31 29 29 30 33

Relation activity -0. 031 0. 120 0. 240 0,342 0. 654

Memory score 32 31 35 34 33

"Memory Score" depends on "Brain Activity" so"Memory Score" is theresponse variable y and the "Brain Activity" is the explanatory variable x.

The correlation coefficient r is 0.6769

R-Squared = 0.4582

The regression equation is

Memory score = 31.70 + 4.180 * Relative activity Based on the correlation r the predictions of Memory Score are (very good, good, bad)

The percent of variation of Memory Score that can be explained by Relative Activity is % (Round to the nearest whole number)

The slope of the regression line is

Using the definition of slope we can describe the relationship between "Memory Score" and "Brain Activity" as follows.

As increases by 1 unit, increases by .

(Recall that the predicted value of Memory Score is what we get from the equation, and the actual or observed value is what we get from the table in which we record the values of the experiment.

The predicted Memory Score when the relative activity -0.031 is (Round to two decimal places) and the actual/observed value is . note that the regression line does not have pass through a point on the scatter plot.

We will only be able to use the regression equation to make predictions of memory score for Relative Activity between nd . That is, we cannot plug in a number outside this range into the the regression equation to make a prediction