Stat 2000: Tips for Web Assign HW 09
Published: Thu, 03/31/11
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General Tips for Web Assign and JMP
When working with Web Assign, always enter the answer to one specific box and then click "Submit Answer" to confirm that is correct before you move on to another box. Do not enter several answers all at once in several boxes before you click "Submit Answer". You risk being marked wrong due to some typo or something.
For some strange reason, JMP 8 occasionally computes wrong answers even if you have copied and pasted your data correctly. I suggest that, if it is feasible, type the given data into your calculator (in Stat mode as shown in Appendix D of my book), and have your calculator compute the sample mean. Compare that answer with JMP's answer for the sample mean. If they are the same, everything is fine. If they are not the same, close JMP 8 and restart it, recopy and paste the data, and check again. Sometimes you have to do this 2 or 3 times before JMP finally works. If it is not feasible to use your calculator to compute the sample mean, have JMP do the question 2 or 3 times, being sure to restart JMP and recopy the data each time, and confirm that JMP gives you the same answer each time before risking entering the results into Web Assign.
If you are taking the course by distance/online (Section D01) click here to see your tips for HW 09.
Continue to study Lesson 10, especially the section on Multiple Linear Regression that begins after question 3.
Note, the values you get for your coefficients and
their test statistics in a multiple linear regression are likely to be
different than the values you would get if you did a simple linear
regression of y versus just one of the explanatory variables. That is
because a simple linear regression looks at the effect that one
explanatory variable alone has on y, while a multiple linear regression
looks at the effect a particular explanatory variable has on y while
holding all the other explanatory variables constant (in a sense,
filtering out the effects of other explanatory variables). In a simple
linear regression, you could always find r, the correlation coefficient,
by square rooting r-squared as given by JMP, but remember r can be
positive or negative (r always has the same sign as b, the slope). In
multiple linear regression, r no longer has much meaning since the model
is using several explanatory variables, but you could still compute it
by square rooting r-squared as given by JMP. In multiple linear
regression, r is always considered to be positive since it is unable to
isolate the effects of any particular explanatory variable and it is
always possible that some of the explanatory variables have a negative
association with y while others have a positive association.
Question 1: Just read
off the appropriate values from the given tables. Note that the proportions they are asking for are the appropriate r-squared values. Review Lesson 9, question 1(d) for the proper interpretation of the coefficient of determination. When they ask for the "additional proportion" in part (d), they are merely asking you for the difference between the two appropriate r-squared values. Recall the formula to compute the
coefficient of determination from an ANOVA table (see my Lesson 10,
question 3 part (a)). Note that (h) is just
a very tricky way of asking you for the confidence interval for the
appropriate coefficient (slope).
You will use JMP for question 2.
Open a "New Data Table" and copy and paste in the given data set. If
you are using JMP 8, be sure to select "Edit" and "Paste with Column
Names". Double-click the HRS, MAIL, CHQ, and CSH column names and make sure
their Data Type is Numeric and their Modeling Type is Continuous.
Select
"Analyze" then "Fit Model" and select HRS and click the "Y" button to
make it a Y. Select the remaining columns and click the "Add" button to
add them as explanatory variables in the model. Make sure the
"Personality" drop-down list is set at Standard Least Squares. If it is
not, and it is not even available as an option, your data has been
corrupted. Go back to the data spreadsheet, double-click on each of
the columns, and make sure their Data Type is Numeric and their
Modeling Type is Continuous and try this again. Click "Run Model" to
have it perform the multiple linear regression. Everything you need is
in the Parameter Estimates. (See my question 4 in Lesson 10 for an
example of how to read the various outputs.)
Question 3: Study Lesson 11 in my book to learn how to perform the Sign Test. Note that what they are calling Y, the test statistic, is what I call k. You have to be a mind-reader to know whether they chose to count the + signs or the - signs. My guess is they chose to count + signs. Regardless of what they make you do to answer part (b), follow my technique to compute the P-value.
Study Lesson 6 in my study book to prepare for this assignment. Those of you with an older edition will study Lessons 6 and 7 (and really only study about the first two questions of Lesson 6, then move on to Lesson 7: The Binomial and Poisson Distributions).
This assignment is all standard Binomial and Poisson distribution questions. Note, in question 1, for a situation to be binomial, you must be able to list the parameters n and p. In addition, X must be able to have values 0, 1, 2, ... n where X is counting the number of "yeses". For a situation to be Poisson, you must be able to list the parameter λ, the average rate, and X must be able to have values 0, 1, 2, all the way to infinity, where X is counting the number of whatever "things" for which you have the average rate.
Question 6 is actually a Sign Test question (taught in Lesson 11 of my book). To get the P-value, for a lower-tailed test, find the probability of the given X value or lower. For an upper-tailed test, find the probability of the given X value or higher. If the test is two-tailed, find the probability of the appropriate tail and double it.