Here are some data which show the tragic consequences of feeding rice to birds:
ID: 3226052 • Letter: H
Question
Here are some data which show the tragic consequences of feeding rice to birds: avian explosions. It’s still commonly believed that throwing rice at weddings causes birds to explore. Here are data from four weddings:
Pounds of thrown rice (x)
Number of exploding birds (y)
3
4
5
6
7
7
7
8
The next few questions will require you to compute R2
and perform an F test.
First, what is the total sum of squares (SStotal)?
more than 9
Let’s fit a least-square regression equation y=a+bx with this data. What is the estimated coefficient a?
more than 1.8
Let’s say your fitted regression equation for these data is y=1.5+0.8636x. What is the predicted value for the first observation where x=3?
more than 3.8
What is the regression (model) sum of squares (SSregression)?
between 7 and 9
And what’s the residual sum of squares (SSresidual)?
more than .9
And what is R2 for these data?
more than .9
Next we’ll use the sums of squares we just computed to calculate F, a test for R2. First off, what kind of statistical test is F?
none of the above
What’s the model (or regression) degrees of freedom, the denominator for calculating the model mean square?
5
What’s the residual (or error) degrees of freedom, the denominator for calculating the residual/error mean square?
5
What’s the model mean square?
more than 9
What’s the error mean square?
more than .9
Using the numbers you’ve calculated for the past two questions, calculate F.
more than 29
Suppose you have calculated an F-value of 30. Given the degrees of freedom are F(1,2), what is the p-value of the F test on whether the R2 is different from zero? You need to use Excel to answer this question.
more than .09
Pounds of thrown rice (x)
Number of exploding birds (y)
3
4
5
6
7
7
7
8
Explanation / Answer
SStotal is between 7 and 9
Coefficient a=between 1.4 and 1.6
Predicted value=1.5+0.863*3=4.089 = more than 3.8
SSregression = between 7 and 9
SSresidual= between 0.5 and 0.7
R2=more than 0.9
F=a one tail test
Model df=1
Residual df=2
Model MS=between 7 and 9
Error MS=less than 0.3
F=more than 29
p-value=between 0.03 and 0.05
SUMMARY OUTPUT Regression Statistics Multiple R 0.968329664 R Square 0.937662338 Adjusted R Square 0.906493506 Standard Error 0.522232968 Observations 4 ANOVA df SS MS F Significance F Regression 1 8.204545455 8.204545455 30.08333333 0.031670336 Residual 2 0.545454545 0.272727273 Total 3 8.75 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1.5 0.904534034 1.658312395 0.23911409 -2.391895829 5.391895829 Pounds of thrown rice (x) 0.863636364 0.157459164 5.484827557 0.031670336 0.18614426 1.541128467Related Questions
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