Stat 2000 Tips for Assignment 5
Published: Tue, 11/16/10
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Throughout the term I will send you all sorts of tips to help you study and learn the course. You probably already have done so, but, if not, I strongly recommend you purchase my Basic Stats 2 Study Book. You will find it a great resource to learn the course. I pride myself in explaining things in clear, everyday language. I also provided numerous examples of all the key concepts with step-by-step solutions. You can order my book at UMSU Digital Copy Centre at University Centre at UM campus. They make the book to order so please allow one business day. The book is split into two volumes and each volume costs $45 + tax.
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Tips for Assignment 5: Goodness of Fit and Simple Linear Regression
Study Lessons 8, 9 and 10 up to the end of question 3, in my book, if you have it, to prepare for this assignment.
I think you will find my questions in Lesson 8 about Goodness of Fit (questions 5 to the end) are very similar to your first three assignment questions, so I don't anticipate any difficulties.
Note, when they have you compute and fill in the "Expected Counts", the last expected value you enter must always make the total come out to exactly the same as the total of the "Observed Counts". This is especially important in the Poisson question where your last cell is X ≥ 6. In a question like that, keep in mind the probabilities for each cell must have a total of 1 (which is to say, the percentages must add up to 100%), so you could always fill in the last percentage without recourse to any formula. That will most likely ensure the expected counts end up with the same total as the observed counts.
Also, make sure you are following your rule about expected counts. Which is to say, if an expected count is less than 5, you must combine its cell with one or more adjoining cells to properly work out the chi-square statistic and the degrees of freedom.
The rest of the assignment uses the concepts I teach in Lessons 9 and 10.
Question 4 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.
Question 5 gives you all the info you need to compute the confidence intervals for the slope. I give you the appropriate formula in Lesson 10.
You will use JMP for question 6. Open a "New Data Table" and create three columns. Name the first column "Sex", the second column "Speed", and the third column "Stride rate". 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, typing "female" or "male" as appropriate in the "Sex" column. Obviously, enter in all the female data first, then all the male data. Now, on the left of the spreadsheet where it numbers all the rows, click and drag to select all the rows that have "female" scores Now select "Rows" and "Markers" and choose whatever marker you want to represent the females. Now, click and drag to select the "male" rows and select a marker to use for them. Click in the top left corner of the spreadsheet (right above row 1) to deselect the rows and we are now ready to analyze the data.
Question 6(a) and (b): Select "Analyze" then "Fit Y by X". They never make it clear which is x and which is y in this problem, but it appears they want x to be speed and y to be stride rate, so select "Stride rate" and click "Y, Response" and select "Speed" and click "X, Factor". Click OK. You will now see a scatterplot with the two different markers plotted distinguishing the female and male scores. 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 6(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 (or just the residuals column) and paste into your file ready for upload.
Question 6(d): Click the red triangle next to "Linear Fit" and select "PlotResiduals". I have no idea what they are getting at in this question. You would expect to see some obvious pattern like the males tend to have positive residuals and the females have negative residuals, or something that makes the females look different from the males, but good luck seeing anything here.
Question 6(e): JMP already did this test for you when you selected "Fit Line". The ANOVA table and the "Parameter Estimates" for the "Stride rate" are giving you all the info you need, but be sure to write out your hypotheses and conclusion in the file you are uploading.
Question 7(a): Copy and paste your data into a "New Data Table" being sure to select "Edit" and "Paste with column names" if you are using JMP 8. Select "Analyze" then "Distribution", highlight both columns and click "Y, Columns" then click OK. The "Moments" give you the means and standard deviations they request.
Question 7(b): Select "Analyze" then "Fit Y by X". Assign x and y as they have indicated in part (a). Click OK. Click the red triangle next to "Bivariate Fit ..." and select "Fit Line" to have JMP compute and graph the least-squares regression line. You will see the least-squares regression equation directly below "Linear Fit". I assume they want the t statistic for the correlation which is also the t statistic for the slope which you can read off the "Parameter Estimates" (See my question 3 in Lesson 10 for how to read the printouts.) Note, JMP gives us the coefficient of determination, r-squared which we can easily change into r. Remember, r always has the same sign as the slope.
Question 8: Use the same approach used in question 7 to get all the info they request. Note, you will use the "Parameter Estimates" to get the slope and its standard error, but then finish computing the confidence interval yourself.