Name: 1 . (6 pts) Explain how the uses we put correlation and linear regression to are similar and explain how they are different. 2 . (30 pts) Below are a set of heights (in inches) and GPA scores for a sample of 6 students. Height GPA 60 4.0 55 3.2 62 3.7 58 3.9 49 2.4 61 2.8 a. Find the correlation coefficient (r) for these two variables by hand: b. Find the mean and standard deviation for each variable c. Find the equation of the regression line to predict GPA from height by hand: d. Find the equation of the regression line to predict height from GPA by hand and: e. Based on this data, what is the GPA prediction for a student who is 56 inches tall? f. How good is this prediction? 3 . (20 pts) Below is a set of sample data containing the ages and Depression scores (0-100, where 100 means most Depressed) of 8 people. Age 18 51 34 22 60 76 28 49 DEP 97 44 75 89 38 54 80 60 a. Are these two variables related? If so, explain how they are related (to what extent and direction? HINT: use statistical evidence to support your answer) b. Predict the Depression score of a 42-year-old. c. Is this a good prediction? Why or why not (hint: use statistics to support your answer)? d. Predict the age of a person who has a Depression score of 100. 4 . (15 pts) For the following data used to predict number of yearly doctors' visits from number of pets owned: Pets 6 12 2 7 Doc Visits 11 2 1 12 a. Find the slope b. Find the intercept c. Write out the equation of the regression line and predict the number of yearly doctors' visits for a person who owns 0 pets. 5 . (12 pts) Using the data from question 4, assume you are now interested in predicting number of pets owned from number of yearly doctors' visits: a. Find the slope b. Find the intercept d. Write out the equation of the regression line and predict the number of pets owned for a person who visits the doctor 50 times a year. 6 . (5 pts) In the following data set, the equation of the regression line to predict GPA from Age is y = .15x-.08. This line predicts that a person who is 23 years old will have a GPA of 3.27. However, looking at the data itself, a 22-year-old has a 3.9 GPA and a 25-yearold has a 3.6 GPA, so shouldn't a 23-year-old have a GPA which is somewhere between 3.6 and 3.9? Explain why this prediction comes about (and makes sense), given the relationships we see in the data. Age 30 18 25 22 8 . GPA 4.0 2.0 3.6 3.9 (12 pts) A health research institute collects information from 20 individuals on the number of years they have spent smoking cigarettes, and their age of death. The data is summarized below: x = 235 y = 1642 xy = 17641 x2 = 6327 Find the correlation coefficient (r): y2 = 135728 SSx = 3565.75 SSy = 919.8