Stat 2000: Tips for Web Assign HW 08
Published: Wed, 03/30/11
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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 08.
Study
Lesson 9 to review the principles of Linear Regression in my study book
then Study Lesson 10 at least up to the end of question 3 to prepare
for this assignment. You do not need to study the section on
Multiple Linear Regression at this time.
Question 1 is
just an algebra problem, they have given you a value for x, y and the
slope and you can use that to compute the intercept. Note, they have
written out the least-squares regression equation for you, and all you
have to do is enter the values for the intercept and slope into the
boxes.
You will use JMP for question 2. Open a "New Data Table" and
create two columns. Name the first column "Beers" and the second column
"BAC". Remember, to create a new
column, simply double-click in the space at the top of the column, to
the right of a pre-existing column. Enter in your data.
Question 2(a) and (b):
Select "Analyze" then "Fit Y by X". Select "BAC" and click "Y, Response"
and select "Beers" and click "X, Factor". Click OK. You will now see a
scatterplot. Click the red triangle next to "Bivariate Fit
..." and select "Density Ellipse" and click on ".99" (it is irrelevant what number you select). An ellipse shows up on your scatterplot, but, more importantly, an output called "Correlation" appears below the scatterplot. Click the blue triangle next to that to reveal the means, standard deviations and correlation for this problem. Click the red triangle next to "Bivariate Normal Ellipse" below the scatterplot and deselect "Line of Fit" to make that ellipse disappear on the scatterplot.
Click the red triangle next to "Bivariate Fit
..." and select "Fit Line" to have JMP compute and graph the
least-squares regression line. Select and copy the printout and paste
into a file ready for upload.
Question 2(c):
Click the red triangle next to "Linear Fit" and select "Save
Residuals". JMP will now add a fourth column to your spread sheet
called "Residuals Stride rate". Select and copy the entire data table and paste into your file ready for
upload. They do not make it clear whether they actually want you to
include the residuals in your upload, but why ask you to compute them
then?
Question 2(d):
Click the red triangle next to "Linear Fit" and select
"PlotResiduals". Remember what I tell you back in Lesson 9, question 1 about residuals.
Question 2(e):
JMP already did this test for you when you selected "Fit Line". The
ANOVA table and the "Parameter Estimates" for the "BAC" are
giving you all the info you need, but be sure to write out your
hypotheses and conclusion in the file you are uploading. You can
determine if there is a linear relationship by either testing the
hypothesis about zero correlation or a hypothesis about zero slope. JMP
gives us the latter in the ANOVA and Parameter Estimates, so I would do
the zero slope hypothesis. I show you how to read these outputs in my
question 3 of Lesson 10.
Question 3 is a good run through of what the ANOVA tells us. I show you how to fill in the table in Lesson 10, question 3 and discuss all the things you can learn from the ANOVA in Lesson 10.
Question 4 gives you all you need to test hypotheses about the correlation. Again, this is discussed in Lesson 10. In part (b), when they ask you to discuss why the conclusion will be different, ask yourself what is the only thing that is different in the two cases.
Question 5(a) and (b): Open a "New Data Table" and enter the given data. Follow the same steps as you did in question 2 above to get the regression line.
Question 5(c), (d), and (e):
JMP does not give you the correlation, but it does give you the coefficient of determination, r-squared. Compute r from that. Remember, r always has the same sign as the slope. Click the red triangle next to
"Linear Fit" and select "Confid Curves Fit" and "Confid Curves Indiv" to have JMP plot the required confidence intervals.
Question 5 (f), (g) and (h): This has to be done by hand using the information from the printouts. Again, I show you how to do all this in Lesson 10, especially question 3.
Question 5 (i): You should know what that ratio is computing and therefore how to interpret it. I teach you how to interpret the coefficient of determination in Lesson 9, question 1 (d).
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.
You will use JMP for question 1. 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 GPA, IQ and Concept column names and make sure their Data Type is Numeric and their Modeling Type is Continuous.
Question 1(a): Select "Analyze" then "Multivariate Methods" then "Multivariate". Select the GPA, IQ and Concept columns and click the "Y, Columns" button to make them all Y columns, click OK. That takes you to an output that shows a correlation matrix where you can read off the desired correlations. Note, when they ask for the proportion of total variation they are asking for the coefficient of determination, r-squared (see my Lesson 9, question 1 part (d) for a discussion of the coefficient of determination).
Question 1(b): Select "Analyze" then "Fit Model" and select GPA and click the "Y" button to make it a Y. Select both IQ and Concept 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 GPA, IQ and Concept 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 1(c): They just want the coefficient of detemination again that you just gave in part (a). The additional percentage is just the difference between that coefficient of determination and the new coefficient of determination your multiple linear regression model now has (given in the Summary of Fit).
Question 1(d): I think they are wanting you to do the t test for the Concept coefficient here which is given in the Parameter Estimates.
Question 2: Just read off the appropriate values from the given tables. Note that (h) is just a very tricky way of asking you for the confidence interval for the appropriate coefficient (slope). Recall the formula to compute the coefficient of determination from an ANOVA table (see my Lesson 10, question 3 part (a)).
Question 3: Copy and paste the data into JMP just as in question 1, then perform a multiple linear regression using "Fit Model" as shown in question 1 above. Parts b, c and d are asking you for the relevant outputs in the JMP tables. Parts a, e and f you are doing by hand. Again, make sure you double-click all the column names and confirm their Data Type is Numeric and their Modeling Type is Continuous before you do the JMP analysis.