WEEK 7 – EXERCISES (you are almost there!)
Enter your answers in the spaces provided. Save the file using your last name as the beginning of the file name (e.g., ruf_week7_exercises) and submit via the Drop Box. When appropriate, show your work.
1. A study was completed that examined the relationship between coffee consumption and level of stress for a group of 50 undergraduates. The correlation was .373, and it was a two-tailed test, done at the .01 level of significance. First, is the correlation significant? Second, what’s wrong with the following statement? “As a result of the data collected in this study and our rigorous analyses, we have concluded that if you drink less coffee, you will experience less stress.”
2. Use the following set of data to answer the following questions.
a. Compute the correlation between age in months and number of words known.
b. Test for the significance of the correlation at the .05 level of significance.
c. Go way back and recall what you learned about correlation coefficients and interpret this correlation.
Age in Months Number of Words Known
12 7
15 9
9 3
7 8
18 15
24 20
15 6
16 8
21 15
15 19
4. Monica is interested in predicting how many 75-year-olds will develop Alzheimer’s disease and is using as predictors level of education and general physical health graded on a scale from 1 to 10. But she is interested in using other predictor variables as well. Answer the following questions.
a. What criteria should she use in the selection of other predictors? Why?
b. Name two other predictors that you think might be related to the development of Alzheimer’s disease.
c. With the four predictor variables (level of education and general physical health, and the two new ones that you name), draw out what the model of the regression equation would look like. (Do your best to draw on Word or describe it in detail).
5. Peter was curious to know if the average number of games won in a year predicts Super Bowl performance (win or lose). The X variable was the average number of games won during the past 10 seasons. The Y variable was whether the team ever won the Super Bowl during the past 10 seasons. Here are the data:
Team Average Number of Wins Over 10 Years Bowl? (1 = yes and 0 = no)
Savannah Sharks 12 1
Pittsburgh Pelicans 11 1
Williamstown Warriors 15 0
Bennington Bruisers 12 0
Atlanta Angels 13 0
Trenton Terrors 16 1
Virginia Vipers 15 1
Charleston Crooners 9 1
Harrisburg Heathens 8 0
Eaton Energizers 12 1
a. How would you assess the usefulness of the average number of wins as a predictor of whether a team ever won a Super Bowl?
b. What’s the advantage of being able to use a categorical variable (such as 1 or 0) as a dependent variable?
c. What other variables might you use to predict the dependent variable, and why would you choose them?
6. Now for multiple predictor variables. Take a look at the data below with the outcome being a great chef. We suspect that variables such as number of years of experience cooking, level of formal culinary education, and number of different positions (sous chef, pasta station, etc.) all contribute to rankings or scores on the Great Chef Test.
Years of Experience Level of Education # of Positions Score on Great Chef Test
5 1 6 89
6 2 3 68
12 3 12 56
21 3 8 88
7 2 5 97
9 1 9 90
13 2 8 79
16 3 9 85
21 2 9 60
11 1 4 89
15 2 8 90
15 3 7 76
1 3 3 78
17 2 6 98
26 2 8 91
11 2 8 88
18 3 7 90
31 3 12 98
27 2 16 88
a. Which are the best predictors of the Chef’s score?
b. What can you expect for a score from a person with 11 years of experience and a Level 2 education, and who has held five positions?
The deadline for this assignment is 11:59 PM EST on Sunday of Week 7
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