It is said that if someone is more left-brained they are more analytical and verbal, whereas a more right-brained person is more visual and intuitive. Student researchers used an 30-second online brain test that determines whether a person is left-brained or right-brained and gives percentages for each. The student researchers were curious whether these percentages change as a person ages. They gave 89 college students this test, recording their ages and their left-brain percentages. The results are shown in the Exercise 10.CE.6 regression output. 

a. Use the regression output to determine the equation of the least squares regression line. Identify all variables used in the equation. 

b. Can a theory-based test for slope be carried out on these data? Explain. 

c. What is the value of the slope of the least squares regression line, and what does it mean in terms of age and left-brain percentage? 

d. What is the value of the coefficient of determination, and what does it mean in terms of age and left-brain percentage? 

e. Use the regression model to predict the left-brain percentage for someone who is 18 years old. 

f. One of the 18-year-old subjects’ test results gave him a left-brain percentage of 31%. Calculate the residual for this subject and explain what it means. 

g. Does age appear to be a useful predictor of left-brain percentage for these subjects? Explain.