Understandable Statistics: Concepts and Methods
12th Edition
ISBN: 9781337119917
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
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Textbook Question
Chapter 9.4, Problem 4P
For Problems 3-6, use appropriate multiple regression software of your choice and enter the data. Note that the data are also available for download at the Companion Sites for this text.
4. Education: Exam Scores Professor Gill has taught general psychology for many years. During the semester, she gives three multiple-choice exams, each worth 100 points. At the end of the course, Dr. Gill gives a comprehensive final worth 200 points. Let x1, x2, and x3 represent a student’s scores on exams 1, 2, and 3, respectively. Let x4 represent the student’s score on the final exam. Last semester Dr. Gill had 25 students in her class. The student exam scores are shown on the next page.
Since Professor Gill has not changed the course much from last semester to the present semester, the preceding data should be useful for constructing a regression model that describes this semester as well.
- (a) Generate summary statistics, including the
mean and standard deviation of each variable. Compute the coefficient of variation (see Section 3.2) for each variable. Relative to its mean, would you say that each exam had about the same spread of scores? Most professors do not wish to give an exam that is extremely easy or extremely hard. Would you say that all of the exams were about the same level of difficulty? (Consider both means and spread of test scores.) - (b) For each pair of variables, generate the sample
correlation coefficient r. Compute the corresponding coefficient of determination r2 Of the three exams 1,2, and 3, which do you think had the most influence on the final exam 4? Although one exam had more influence on the final exam, did the other two exams still have a lot of influence on the final? Explain each answer. - (c) Perform a
regression analysis with x4 as the response variable. Use x1 x2, and x3 as explanatory variables. Look at the coefficient of multiple determination. What percentage of the variation in x4 can be explained by the corresponding variations in x1 x2, and x3 taken together? - (d) Write out the regression equation. Explain how each coefficient can be thought of as a slope. If a student were to study "extra hard" for exam 3 and increase his or her score on that exam by 10 points, what corresponding change would you expect on the final exam? (Assume that exams I and 2 remain "fixed" in their scores.)
- (e) Test each coefficient in the regression equation to determine if it is zero or not zero. Use level of significance 5%. Why would the outcome of each hypothesis test help us decide whether or not a given variable should be used in the regression equation?
- (f) Find a 90% confidence interval for each coefficient.
- (g) This semester Susan has scores of 68, 72, and 75 on exams 1, 2, and 3, respectively. Make a prediction for Susan’s score on the final exam and find a 90% confidence interval for your prediction (if your software supports prediction intervals).
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Students have asked these similar questions
The following ordered data list shows the data speeds for cell phones used by a
telephone company at an airport:
A. Calculate the Measures of Central Tendency from the ungrouped data list.
B. Group the data in an appropriate frequency table.
C. Calculate the Measures of Central Tendency using the table in point B.
D. Are there differences in the measurements obtained in A and C? Why (give at
least one justified reason)?
I leave the answers to A and B to resolve the remaining two.
0.8
1.4
1.8
1.9
3.2
3.6
4.5
4.5
4.6
6.2
6.5
7.7
7.9
9.9
10.2
10.3
10.9
11.1
11.1
11.6
11.8
12.0
13.1
13.5
13.7
14.1
14.2
14.7
15.0
15.1
15.5
15.8
16.0
17.5
18.2
20.2
21.1
21.5
22.2
22.4
23.1
24.5
25.7
28.5
34.6
38.5
43.0
55.6
71.3
77.8
A. Measures of Central Tendency
We are to calculate:
Mean, Median, Mode
The data (already ordered) is:
0.8, 1.4, 1.8, 1.9, 3.2, 3.6, 4.5, 4.5, 4.6, 6.2, 6.5, 7.7, 7.9, 9.9, 10.2, 10.3, 10.9,
11.1, 11.1, 11.6,
11.8, 12.0, 13.1, 13.5, 13.7, 14.1, 14.2, 14.7, 15.0, 15.1, 15.5,…
PEER REPLY 1:
Choose a classmate's Main Post.
1. Indicate a range of values for the independent variable (x) that is reasonable
based on the data provided.
2. Explain what the predicted range of dependent values should be based on
the range of independent values.
In a company with 80 employees, 60 earn $10.00 per hour and 20 earn $13.00 per
hour.
Is this average hourly wage considered representative?
Chapter 9 Solutions
Understandable Statistics: Concepts and Methods
Ch. 9.1 - Statistical Literacy When drawing a scatter...Ch. 9.1 - Prob. 2PCh. 9.1 - Prob. 3PCh. 9.1 - Prob. 4PCh. 9.1 - Prob. 5PCh. 9.1 - Prob. 6PCh. 9.1 - Prob. 7PCh. 9.1 - Prob. 8PCh. 9.1 - Prob. 9PCh. 9.1 - Critical Thinking: Lurking Variables Over the past...
Ch. 9.1 - Prob. 11PCh. 9.1 - Prob. 12PCh. 9.1 - Prob. 13PCh. 9.1 - Health Insurance: Administrative Cost The...Ch. 9.1 - Prob. 15PCh. 9.1 - Geology: Earthquakes Is the magnitude of an...Ch. 9.1 - Prob. 17PCh. 9.1 - Prob. 18PCh. 9.1 - Prob. 19PCh. 9.1 - Prob. 20PCh. 9.1 - Prob. 21PCh. 9.1 - Prob. 22PCh. 9.1 - Prob. 23PCh. 9.1 - Prob. 24PCh. 9.2 - Statistical Literacy In the least-squares line...Ch. 9.2 - Prob. 2PCh. 9.2 - Critical Thinking When we use a least-squares line...Ch. 9.2 - Prob. 4PCh. 9.2 - Prob. 5PCh. 9.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 9.2 - Prob. 7PCh. 9.2 - For Problems 718, please do the following. (a)...Ch. 9.2 - Prob. 9PCh. 9.2 - For Problems 718, please do the following. (a)...Ch. 9.2 - Prob. 11PCh. 9.2 - Prob. 12PCh. 9.2 - For Problems 718, please do the following. (a)...Ch. 9.2 - Prob. 14PCh. 9.2 - Prob. 15PCh. 9.2 - For Problems 718, please do the following. (a)...Ch. 9.2 - Prob. 17PCh. 9.2 - Prob. 18PCh. 9.2 - Prob. 19PCh. 9.2 - Residual Plot: Miles per Gallon Consider the data...Ch. 9.2 - Prob. 21PCh. 9.2 - Prob. 22PCh. 9.2 - Prob. 23PCh. 9.2 - Prob. 24PCh. 9.2 - Prob. 25PCh. 9.3 - Prob. 1PCh. 9.3 - Prob. 2PCh. 9.3 - Prob. 3PCh. 9.3 - Prob. 4PCh. 9.3 - Prob. 5PCh. 9.3 - Prob. 6PCh. 9.3 - Prob. 7PCh. 9.3 - In Problems 712, parts (a) and (b) relate to...Ch. 9.3 - Prob. 9PCh. 9.3 - Prob. 10PCh. 9.3 - In Problems 712, parts (a) and (b) relate to...Ch. 9.3 - Prob. 12PCh. 9.3 - Prob. 13PCh. 9.3 - Prob. 14PCh. 9.3 - Prob. 15PCh. 9.3 - Expand Your Knowledge: Time Series and Serial...Ch. 9.3 - Prob. 17PCh. 9.4 - Statistical Literacy Given the linear regression...Ch. 9.4 - Prob. 2PCh. 9.4 - For Problems 3-6, use appropriate multiple...Ch. 9.4 - For Problems 3-6, use appropriate multiple...Ch. 9.4 - Prob. 5PCh. 9.4 - Prob. 6PCh. 9 - Prob. 1CRPCh. 9 - Prob. 2CRPCh. 9 - Prob. 3CRPCh. 9 - Prob. 4CRPCh. 9 - Prob. 5CRPCh. 9 - Prob. 6CRPCh. 9 - Prob. 7CRPCh. 9 - Prob. 8CRPCh. 9 - Prob. 9CRPCh. 9 - Prob. 10CRPCh. 9 - Prob. 1DHCh. 9 - Prob. 1LCCh. 9 - Prob. 1UTCh. 9 - Prob. 2UTCh. 9 - Prob. 3UTCh. 9 - Prob. 4UTCh. 9 - Prob. 5UTCh. 9 - Prob. 6UTCh. 9 - Prob. 7UTCh. 9 - In Problems 16, please use the following steps (i)...Ch. 9 - Prob. 2CURPCh. 9 - Prob. 3CURPCh. 9 - Prob. 4CURPCh. 9 - Prob. 5CURPCh. 9 - Prob. 6CURPCh. 9 - Prob. 8CURPCh. 9 - Linear Regression: Blood Glucose Let x be a random...
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