Test II STA 3024 D. Meeter Sp '01 Name_______________________

EITHER work all problems on this paper OR all on separate paper. LABEL your work. This is a test. Do your own work (and show it.) QUESTIONS? Ask ME. DUE April 17.

On multiple choice questions, pick all of the statements that apply (possibly none.)

"Statistically adequate" means "appears to satisfy Assumptions A1-A4, according to our checks..

1. A regression model

  1. may have a high R2 even though the model is statistically inadequate

  2. may be statistically inadequate even though every regression coefficient is significant, p < 0.05.

  3. may have a very low R2 even though the model is statistically adequate

  4. will never have a lower R2 if we add another term to the model

  1. The sample correlation r between y and x

  1. equals zero if H0: r = 0 is correct

  2. if statistically significant, demonstrates that x and y are causally related

  3. will not change if all x and y values have 1,323 added to them

  4. can be zero even if there is a strong relationship between y and x in the data

  1. When adding x2 to a linear regression of y on x1,

  1. b1 will change if x1 and x2 are correlated

  2. SSE + SSreg will remain the same

  3. SSE will never increase

  4. b1 may no longer be statistically significant, or may become more significant

4. From a multiple regression:

Source SS df There are 30 observations. The regression of y on x2 alone

Due to x1 200 1 yielded SSE = 1,400. The total SS, with 29 d.f., is 1,800.

Extra due to x2 300 1

Extra due to x3 400 1 a) Calculate SSE for the above table.

b) Estimate s 2 in the full (three-variable) regression

c) Test H0: b 3 = 0 using a partial F test.

d) Calculate SSreg in the regression of y on x2 alone.

  1. In a regression of y = leg strength on x = body weight, two species were studied. The reference species was A. The fitted equation was

    2. .

    a) Assuming that all coefficients are significant, what is the prediction equation for Species B?

    b) How much is the intercept for Species A different from that of Species B?

    c) Suppose that 0.6 was not significantly different from zero. Interpret the fitted equation, using words from this particular problem, e.g. strength, species, weight.

    d) What does c) have to do with ANCOVA?

  2. The fitted equation was

    3. What is the fitted equation in terms of y? You can assume either natural or common logs.

    Given Minitab output, describe how could you test whether y was proportional to x.

  3. The dependent variable was College GPA; the independent variable was SAT score. The data was taken on history majors and biology majors. Draw a scatterplot which illustrates

 

 

  1. Biology majors average the same GPA as History majors, but after adjusting for SAT, Biology Majors have higher GPAs.

    2.  

     

  2. There is a correlation between GPA and SAT within each of the two groups, but when they are put together (approximately equal sample sizes) the correlation goes away.

    3.  

     

  3. Biology majors average higher GPAs, but after adjustment for SAT, History majors have higher GPAS.

 

  1. Give an example from your field (state field) in which a multiple regression model would be appropriate. Identify all variables; state how the sample is selected.

    2.  

     

  2. Give an example from your field in which ANCOVA would be appropriate. Identify all variables; state how the sample is selected. Do not use the same example as Problem 6, although one could be a special case of the other.

    3.  

     

     

  3. Give an example from your field of data which is usually transformed before it is statistically analyzed, and state why the transformation is used.

    4.  

  4. In the article by Walter Tschinkel, explain how, in your opinion, he used regression to come up with the first two conclusions noted with ■. Find a statistically oriented statement that you agree with (state why.) Find a statistically oriented statement that you disagree with (state why.)