Stat 2000: Tips for Assignment 7
Published: Sat, 02/25/12
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There is no Assignment 7 for the Classroom Lecture Sections.
Continue to study Lesson 10 at least up to the end of question 3 to prepare for this assignment.
You do not need to study the section on Multiple Linear Regression at
this time. Note that HW 6, 7 and 8 all deal with concepts from Lesson
10.
Question 1 is
similar to my question 3 in Lesson 10. Note, by s, the standard error
points about the regression line, they mean the standard deviation of
the residuals, Se.
Question 2 is
standard stuff. Obviously, watch that they have changed the value of
n. This is demonstrating that, if you choose a large enough sample
size, almost any nonzero r value will be statistically significant (but
perhaps of no practical importance).
You will use JMP for question 3.
Open a "New Data Table" and create two columns. Name the first column
"Diameter" and the second column "Height". 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 the data manually, and we
are now ready to analyze the data. Double-click both column names and
confirm their Data Type is Numeric and their Modeling Type is
Continuous.
Question 3(a) and (b):
Select "Analyze" then "Fit Y by X". You should be able to tell which
is x and which is y. Select the y variable and click "Y, Response" and
select the x variable and click "X, Factor". Click OK. You will now
see a scatterplot. Click the red triangle next to "Bivariate Fit ..."
and select "Fit Line" to have JMP compute and graph the least-squares
regression line. When they tell you to "interpret the regression coefficient," I believe they want you to interpret the slope (since you have just found the slope). The slope can also be called the coefficient, as we see in multiple linear regression.
Question 3(c): JMP gives you the coefficient of determination, r2. Compute r from that value.
Question 3(d) and (e):
Click the red triangle next to "Linear Fit" and select "Confid Curve
Indiv" and "Confid Curve Fit" to get these two intervals they want. As I
tell you in Lesson 10, the curves that are closer to the line are the
confidence intervals for the mean, the outer curves are the prediction
intervals.
Question 3(f):
JMP already did this test for you when you selected "Fit Line". The
ANOVA table and the "Parameter Estimates" are giving you all the
info you need (test statistic and P-value), but be sure to write out your hypotheses and conclusion
in the file you are uploading. You can determine if there is a linear
relationship by either testing the hypothesis about zero correlation or a
hypothesis about zero slope. JMP gives us the latter in the ANOVA and
Parameter Estimates, so I would do the zero slope hypothesis. I show
you how to read these outputs in my question 3 of Lesson 10.
Question 3(g) and (h): These must be computed by hand using the appropriate formulas and numbers from JMP as I show in my question 3 of Lesson 10.
Question 3(i): You
should know what this ratio is computing and how to determine it. I
talk about this in Lesson 10, and show you how to interpret it in
question 1 of Lesson 9.