Stat 1000: Tips for Assignment 4
Published: Sun, 01/29/12
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If you are taking the course by Distance/Online (Sections D01, D02, etc.), click here for my tips for your Assignment 4.
If you are taking the course by classroom lecture (Sections A01, A02, etc.), click here for my tips for your Assignment 4.
Tips for Assignment 4 (Sections A01, A02, etc.)
Tips will be sent once the assignment has been posted.
Study Lesson 2: Regression and Correlation in my book, if you have it, to prepare for this assignment. (In older editions of my book this was Lesson 3.)
Question 1:
To compute the correlation coefficient by hand, follow my
example in Lesson 2, question 1, part (c). Note, you are not given
the means and standard deviations for x and y already, so 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. Put your calculator in Linear Regression Stat Mode (see Appendix D
of my book). After you enter all the (x,y) data points, you can ask it for the mean
and standard deviation of the x values, and the mean and standard
deviation of the y values. For example, Sharps use "RCL 4" to get x-bar
and "RCL 7" to get y-bar. "RCL 5" gives you Sx and "RCL 8" gives you
Sy.
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).
Of course, your calculator actually tells you the value of r, so you
can use that as a check.
Question 2 is just an algebra question.
The empty boxes imply they want you to feed in the value of a, the intercept, and b, the slope. They give you three of x, y, a, and b and want you to figure out the
missing one. Sub the givens into the appropriate places of
y = a + bx and solve what is missing.
Question 3 is a good run through of the formulas I show you in Lesson 3. My question 5 is quite similar, but also make sure you have fully gone through question 1.
Question 4 uses JMP.
Here is how to use JMP for linear regression. First
copy and 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). If
you have to type the data in manually, 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.
Note that you cannot use JMP to make the prediction they request. That is done by hand using the least-squares regression line that JMP found for you, of course. Of course, you, not JMP, are responsible for the interpretations they ask for.