Stat 1000 Tips for Assignments about Linear Regression and Correlation
Published: Fri, 10/08/10
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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 1 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 Assignments about Linear Regression and Correlation
For those of you using Web Assign these tips refer to Assignment 2, I believe. If you are taking the course by distance/online, these tips relate to your Assignment 4. If you are doing good old-fashioned paper hand-in assignments, these tips will help you with part of Assignment 2, I believe (you will also need to look at my tips for Selecting Samples and Designing Experiments).
Study Lesson 3 in my book, if you have it, to prepare for this assignment.
If you are asked to compute the correlation coefficient by hand, follow my example in Lesson 3, question 1, part (c) to see how to compute r by hand. Note, if you are not given the means and standard deviations for x and y already, you are certainly allowed to use the Linear Regression Stat Mode on your calculator to tell you the means and standard deviations of both x and y. Note, only those of you who have my blue or green study book have an example that follows exactly the headings given in this question. For those of you using Web Assign, even though they tell you to do everything to three decimal places, don't do that. Record every single decimal place your calculator gives you for each calculation, or else your answers won't be accurate enough. I suggest you do everything on paper first, then you can type in the results, rounding all of your numbers off to 3 decimal places at that time (even though you actually did the calculations using all the decimal places). Those of you doing the old-fashioned paper assignment are already given rounded off answers for the standard deviations, and you should certainly use them for the rest of the calculations, but understand your answer will probably only be accurate to a couple of decimal places. In your case, I believe your question 1 has you do the entire linear regression analysis (making a scatterplot, graphing the line) by hand, which I show you how to do in my question 1 in Lesson 3.
Here is how to use JMP for linear regression.
If you are using JMP, first paste the data into a New Data Table the usual way (see my previous homework tips if you are not sure how to paste the data). Conversely, or if you are doing an old-fashioned paper assignment, manually type the data in. Simply double-click the space to the right of "Column 1" to create "Column 2". Enter the X data down column 1 and the Y data down column 2. Be sure to double-click each column to give it an appropriate name and to ensure the Data Type is Numeric and the Modeling Type is Continuous.
Select Analyze, then Fit Y By X. Highlight the column you have determined should be X, and click the X, Factor button. Highlight the column you have determined should be Y and click the Y, Response button. Click OK.
You should now see a scatterplot. Click the red triangle above the scatterplot and select Fit Line and JMP will draw in the least-squares regression line. Note, it shows you the regression equation directly below the scatterplot. JMP also shows you the value of r-squared (the coefficient of determination), rather than r, the correlation coefficient. Remember, the coefficient of determination is the percentage of y's variation explained by the regression equation. You can always square root this number to get r, the correlation coefficient, but use your scatterplot to help you decide if r is negative or positive because your calculator can't tell you that.
If you want to get rid of anything, click the red triangle and deselect anything you don't want to see. Note, if you click the blue triangle next to something, that will make part of the output disappear as well, if you wish. Just click the blue triangle again to make it reappear.