Hello all. Thursday is my final exam in undergrad. Regression Analysis, and I
can use some help with these problems. These are actually problems I've gotten
wrong on our first two exams. Keep in mind that this is an undergrad,
non-calculus based course. Any help would be much appreciated!
note: b=beta
1. When estimating the simple linear model (Y=b0+b1x+e), we obtain the
following summary stats: sigma(x-xbar)squared= 27.54,
sigma(x-xbar)(y-ybar)=7.62, sigma(y-ybar)squared=3.56, xbar=3.06, and
ybar=2.12.
The question is, how do I calculate the residual variance (sigma squared) given
this data. I've looked all over my book for an appropriate formula, but they
all seem to be related to other summary statistics.
2. A fashion designer wishes to determine whether the width of yarn (x, in mm)
is related to the strength (y, in amt of force) of the fabric used in her
designs. She wishes to use the general linear test approach to test
H0:b0=20b1=2 vs. Ha:b0not equal to 20 and/or b1=2.
(a) What is the reduced model (that given by H0)? I put y=b0+e
(b) What is the full model (that given by Ha)? I put y=b0+b1x+e
(c) What are the algebreic functions for SSE(full model) and SSE(reduced) and
their degrees of freedom?
I put:
SSE(F)= SSE, df(F)=n-1
SSE(R)=SStotal, df(R)=n-2
3. Given the following ANOVA table:
Source degrees of freedom sum of squares
Model ? 3000
Error 40
Total 4000
Also, Adjusted-Rsquared=.7250
(a) How many independent variables are in the model?'
I know this should come out to be total degrees of freedom for the model.
I have no clue how to get this from the given info. Obviously SSerror is 1000,
but other then that I'm sorta lost. Is some sort of algebraic manipulation
involved here?
(b) How many observations is this analysis based on?
(c) Give the proportion of the variation in the dependant variable that is
'explained' by the independent variables.
Thanks in advance for any assistance.
Adam
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