Stat 1000: Assignment 4 Tips (Distance/Online Sections)
Published: Wed, 01/30/13
My tips for Assignment 4 are coming below, but first a couple of announcements.
Please note that my first two-day review seminar for
Stat 1000 will be on Saturday, Feb. 2 and Sunday, Feb. 3, in room 100 St. Paul's College,
from 9 am to 6 pm each day. This seminar will cover the lessons in Volume 1 of my book.
For more info about the seminar, and to register if you have not done so already, click this link:
Make sure you do: Tips on How to Do Well in Stat 1000
Did you read my Tips on what kind of calculator you should get?
Did you miss my Tips for Assignment 3?
If you are taking the course by Classroom Lecture (Sections A01, A02, etc.), I will send tips for Assignment 4 once it is posted.
Tips for Assignment 4 (Distance/Online Sections D01, D02, D03, etc.)
Don't have my book? You can download a free sample containing Lesson 1 at my website here:
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 A
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.
Here is a link to a
digital copy of that appendix:
For example, after you have entered your (x,y) data points, 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.
A lot of Casio calculators (and some Texas Instruments) use
the "σ" symbol ("sigma," the Greek lowercase "s") to denote "standard
deviation". For example, in many Casios, after you
have entered the data, you first select "S.VAR." You will find it
written above one of your buttons, perhaps above the "2" or nearby on
the keyboard. It is accessed by pressing "SHIFT" then "S.VAR"
(Statistical Variables). Once you select S.VAR, you are shown a menu
where you see the symbol " x̅ " for the sample mean (select "1" and press "=" to get the sample mean). You are also told you can press "2" to get " xσn " or press "3" to get " xσn-1 ". That is Casio's way of
designating the population standard deviation and the sample standard
deviation, respectively. You will always want the sample standard
deviation, Sx, to select " xσn-1 ". Similarly, if you
select S.VAR and then press your right arrow button, you will be
scrolled through other options. For example, you can select " y̅ ", the mean of the y values, or " yσn-1 " to the get Sy, the standard deviation of the y values.
Even though they tell you to do everything to three decimal places, don't do that!
Step 1: Enter all your (x,y) data points into your calculator once you have put it into Linear Regression Stat Mode.
Step 2: Ask your calculator for r, the
correlation coefficient, and enter its value, rounded off to three
decimal places (and make sure you round, don't trim: e.g. 0.6137 rounds
to 0.614) in the box WebAssign provides. If WebAssign says you are
correct, proceed to Step 3. If not, re-enter your data and be more
careful this time. Once you have correctly found r, keep your data in the calculator ready to proceed to Step 3.
Step 3: Ask your calculator for the values of x̅, y̅ , Sx, and Sy. DO NOT ROUND OFF THESE VALUES. KEEP EVERY SINGLE DIGIT YOUR CALCULATOR PROVIDES.
Step 4: ON
PAPER, proceed to calculate and record all the entries you will
eventually type into WebAssign, following my example in question 1(c)
in Lesson 2. Again, write down every
single digit your calculator gives you for each and every calculation.
Find the total of your last column of digits (what WebAssign wants
entered as your SUM) and divide by n - 1 and confirm that you have
calculated the correct value for r.
Step 5: Once you have confirmed that you
were able to compute the correct value of r by hand, enter all the
numbers you computed in Step 4 into the appropriate boxes in WebAssign.
As you enter each number, round it off to three decimal places as
requested.
Question 2 is just an algebra question.
Note that they want you to fill in the empty boxes with the values for a, the intercept, and b, the slope.
HINT: You have a
formula to compute the intercept a, provided you know the slope, b, and
the mean values for x and y (see my question 1(e)). You can use that
formula in this question too, because it works for all values of x and y
that are on the line (i.e. if you already know a predicted y for a
given x, and if you already know b).
Question 3 is a good run through of the formulas and concepts I show you in Lesson 2. Make
sure you are rounding the values to the required number of decimal
places and, use the rounded off numbers to compute any other future
values they require.
Question 4 uses JMP.
Click the "New Data
Table" icon on the toolbar at top left in the JMP home screen. Select
and copy the given data table and then, in JMP, select "Edit" then
select "Paste with Column Names". You should now see two columns
labeled MRK and TIM in your JMP spreadsheet. Be sure to double-click
each
column label (or right-click the column and select "Column Info") and
confirm the Data Type is
Numeric and the Modeling Type is Continuous, changing to those settings
if necessary.
Select "Analyze", then "Fit Y By X". Highlight "TIM", and click the "X, Factor"
button. Highlight "MRK" and click
the "Y, Response" button. Click OK.
You should now see a scatterplot (if you don't, your data is
not properly formatted; go back and check the columns are Numeric and
Continuous as I mentioned above). 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 under "Linear Fit" below the scatterplot. JMP also
shows you the value
of r-squared (the coefficient of determination) in the "Summary of
Fit", 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.
You can read off the answers for the intercept, slope and
coefficient of determination and type them into the appropriate boxes in
WebAssign. Make sure you round off to the requested number of decimal
places in each case.
Use your rounded off answer to the least-squares regression
line you just entered into WebAssign to make the prediction they have
requested and enter it into the box they provide.
They ask you to hid the "Analysis of Variance" part of the output,
so simply click the gray triangle next to it and you will see that part
of the output disappear.
You will need to copy and paste this output into a document
to get ready to add your answers for for part (d) as well. Here is how to do
that:
Click the thin blue line near the top of the window that has
the histogram, etc. to reveal the toolbar. Select the icon that looks
like a fat white cross or plus sign "+". This is your "Selection"
tool. Your mouse cursor should now have changed from an arrow to that
white cross. Click the title bar that says "Bivariate Fit of ..." at the top
of the output and that should select the entire output (scatterplot, Summary of Fit, etc.). Right-click and select Copy.
In your Word document, below the outputs you have pasted in, type in your answers for part (d).
You are now ready to save and upload the file that answers parts (b), (c) and (d). In your Word document (or whatever program you are using), select "File" then "Save As" and select "PDF File". Type in whatever name you want the file to have in the "File name" section. Select which folder you want to save the
file in (I suggest you select "Desktop" so that the file will just
appear write on your desktop home screen. Click
"Save" or "Publish". You should now have your file ready to upload into the
assignment.