Stat 2000: Tips for Assignment 5

Published: Fri, 11/20/15

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Did you see my tips for Assignment 1? Click here.
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Did you see my tips for Assignment 3? Click here.
Did you see my tips for Assignment 4? Click here.
Tips for Assignment 5
Study the Chi-Square Goodness of Fit part of Lesson 9: Chi-Square Tests (in other words the rest of Lesson 9).  You also will need to study Lesson 10: Review of Linear Regression and Lesson 11: Inferences for Linear Regression (up to the end of question 3, you do not need to study the Multiple Linear Regression section at this time). 

Note that they have OMITTED Multiple Linear Regression and Lesson 12: Nonparametric Tests (The Sign Test) this term. None of this appears on the current assignment, and they have omitted these topics every term lately.  DO NOT STUDY THESE SECTIONS.

Remember my advice in the tips above.  Don't start working on the assignment too soon.  Study and learn the lesson first, and use the assignment to test your knowledge.  Of course, always seek out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment.  Learn first, then put your learning to the test.

To type in formulas you are using and to show your numbers subbed into the formulas click the button in the toolbar that looks like the Sigma Summation symbol (you have to click the "..." other options button to see the sigma formula input button.  Then click the various buttons to make your fractions and enter the symbols.

Exception: Always do any JMP stuff open-book.  Have my tips in front of you, and let me guide you step-by-step through any JMP stuff.  JMP is just "busy" work.  The sooner you get it done and can move on to productive things like understanding the concepts and interpreting the JMP outputs, the better off you will be.
Question 1
You will be using Table F for the first two questions.  Here is a link where you can download the table if you have not already done so:

This is not unlike my Lesson 9, question 5.  Make sure you follow their instructions for rounding.  They want the values rounded to two decimal places

They make their goodness-of-fit table horizontally, while I prefer to make mine vertically. 

Note that you can insert a table from the toolbar into your answer box if you want to summarize the results into a table like they provide.  Or, if you find that too annoying (and it is pretty annoying), you could just describe in words where each answer belongs.  Such as Expected Count for Bloc Quebecois is <blank> and The Chi-Square for Bloc Quebecois is <blank>, etc.

If you get a test statistic that goes off the end of the table:
If your chi-square value is so small that it is off the left side of the table, then say the P-value is between 0.25 and 1.  If your chi-square is so large that it is off the right side of the table, say the P-value is between 0 and 0.0005.

Keep this tip in mind for any of your critical value tables.  Always imagine there is an extra column at each end.  The last column is 0 (for very small P-values), and the first column is either .50 (in the case of t) or 1 (in the case of F or chi-square since those two curves are not symmetric).
Question 2
Similar to my Lesson 9, question 8

They also then talk about estimating the parameter later in the problem, parts (h) and (i), which is like my Lesson 9, question 9.
Question 3
This is a runthrough of Linear Regression.  Be sure to study Lessons 10 and 11 in my book before attempting this and the rest of the questions in this assignment.  You should especially work through question 1 in Lesson 10 and questions 1 and 3 in Lesson 11.

Note that part (b) is asking for r-squared, the coefficient of determination as I discuss for the first time in Lesson 10, question 1(d).

Note that they give you SSE, the sum of the squared residuals, so you are able to compute the variance of the residuals (MSE = SSE/DFE).  MSE is your estimate for σ, as requested in part (e).  That is what I call Se, the standard deviation of the residuals, the estimate for σε, the standard deviation of the population of residuals.

Never forget , in a regression context, if they start talking about σ or s, they are referring to the standard deviation of the residuals for the population or sample, respectively.  To add to the confusion, they have also been known to use σ^ to represent Se. 

To do Linear Regression in JMP:
Open a "New Data Table".  Enter all the data for x in Column 1 and all the data for y in Column 2.  Be sure to name the columns appropriately.  Here, Column 1, x, will be Study Time and Column 2, y, will be Score.  Select "Analyze, Fit Y By X".  Highlight Study Time and click "X, Factor".  Highlight Score and click "Y, Response".  Click OK.

You should now be looking at a scatterplot.  Click the red triangle and select Density Ellipse and select 0.99 (it doesn't matter; you don't want this at all, but this gives you a summary of the means, standard deviations, and the correlation coefficient, r).  Click the red triangle that appears below the scatterplot which says Bivariate Normal Ellipse and deselect "Line of Fit" to make the ellipse disappear from your scatterplot.  You will also note that there is a title bar called Correlation below the scatterplot now.  Click the blue triangle to open it up and confirm the means and standard deviations match those you were given.  If not, perhaps you were mixed up which one was x and which one was y?

Click the red triangle and select "Fit Line" to get the least-squares regression line.  You now have all the outputs you need. 

Part (l): 
Be sure to read in Lesson 11 the connection between the t test statistic for the slope and the t test statistic for the correlation.  And also the connection between t for the slope and F for the slope.  Although they want you to do a lot of this question by hand (and you certainly should since that will also happen on the exam), do note that JMP does do a lot of this stuff for you and you can use it to check your answers before you submit them.
Question 4
This is similar to my Lesson 11, question 2.
Question 5
I show you how to fill in an Anova table like this in Lesson 11, question 3.  Otherwise, similar to the previous question.

Again, in part (b), they are asking for the standard deviation of the residuals, Se, which is the square root of MSE.