Stat 2000: Tips for Assignment 8
Published: Thu, 02/23/12
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Continue to study Lesson 10, especially the section on Multiple Linear Regression that begins after question 3.
Note, the values you get for your coefficients and
their test statistics in a multiple linear regression are likely to be
different than the values you would get if you did a simple linear
regression of y versus just one of the explanatory variables. That is
because a simple linear regression looks at the effect that one
explanatory variable alone has on y, while a multiple linear regression
looks at the effect a particular explanatory variable has on y while
holding all the other explanatory variables constant (in a sense,
filtering out the effects of other explanatory variables). In a simple
linear regression, you could always find r, the correlation coefficient,
by square rooting r-squared as given by JMP, but remember r can be
positive or negative (r always has the same sign as b, the slope). In
multiple linear regression, r no longer has much meaning since the model
is using several explanatory variables, but you could still compute it
by square rooting r-squared as given by JMP. In multiple linear
regression, r is always considered to be positive since it is unable to
isolate the effects of any particular explanatory variable and it is
always possible that some of the explanatory variables have a negative
association with y while others have a positive association.
You will use JMP for question 1.
Open a "New Data Table" and copy and paste in the given data set. If
you are using JMP 8, be sure to select "Edit" and "Paste with Column
Names". Double-click the GPA, IQ and Concept column names and make sure
their Data Type is Numeric and their Modeling Type is Continuous.
Question 1(a):
Select "Analyze" then "Multivariate Methods" then "Multivariate".
Select the GPA, IQ and Concept columns and click the "Y, Columns" button
to make them all Y columns, click OK. That takes you to an output that
shows a correlation matrix where you can read off the desired
correlations. Note, when they ask for the proportion of total variation
they are asking for the coefficient of determination, r-squared (see my
Lesson 9, question 1 part (d) for a discussion of the coefficient of
determination).
Question 1(b):
Select "Analyze" then "Fit Model" and select GPA and click the "Y"
button to make it a Y. Select both IQ and Concept and click the "Add"
button to add them as explanatory variables in the model. Make sure the
"Personality" drop-down list is set at Standard Least Squares. If it
is not, and it is not even available as an option, your data has been
corrupted. Go back to the data spreadsheet, double-click on each of
GPA, IQ and Concept and make sure their Data Type is Numeric and their
Modeling Type is Continuous and try this again. Click "Run Model" to
have it perform the multiple linear regression. Everything you need is
in the Parameter Estimates. (See my question 4 in Lesson 10 for an
example of how to read the various outputs.)
Question 1(c): They just want the coefficient of detemination again that you just gave
in part (a). The additional percentage is just the difference between
that coefficient of determination and the new coefficient of
determination your multiple linear regression model now has (given in
the Summary of Fit).
Question 1(d): I think they are wanting you to do the t test for the Concept coefficient here which is given in the Parameter Estimates.
Question 2: Just read off the appropriate values from the given tables. Note that
(h) is just a very tricky way of asking you for the confidence interval
for the appropriate coefficient (slope). Recall the formula to compute
the coefficient of determination from an ANOVA table (see my Lesson 10,
question 3 part (a)).
Question 3: Copy and paste the data into JMP just as in question 1, then perform a
multiple linear regression using "Fit Model" as shown in question 1
above. Parts b, c and d are asking you for the relevant outputs in the
JMP tables. Parts a, e and f you are doing by hand. Again, make sure
you double-click all the column names and confirm their Data Type is
Numeric and their Modeling Type is Continuous before you do the JMP
analysis.