STA 6166 UNIT 4 Section 1 Exercises
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Unit 4 Section 1 Exercises

You can choose to work some or all of the problems listed below. We recommend that you at least work the problems listed in your major area of interest. Answers to this exercise can be found here.(ANSWERS)

General Questions.
  1. What is the analysis objective in regression?
  2. What are the steps in performing a regression analysis?
  3. Write out the functional form for a linear regression model?
  4. What is the difference between a proportional relationship and a linear relationship?
  5. The error term in a linear regression model symbolically represents two types of errors, what are they?
  6. How would you decide what form the relationship among your variables should take? What are least squares parameter estimates?
  7. When we talk about partitioning sums of square, what are we talking about?
  8. What are the two assumptions we make regarding model errors which allow us to perform inferences on model parameters and predictions?
  9. When we test for a significant regression, we compare two competing models, what are they?
  10. Plot a configuration of residuals which would indicate an inadequate regression.
  11. If I found a standardized residual which had value -4.1, what might I conclude?
  12. What characteristic must my data have if I am to attempt to compute a pure error term?
  13. What does r measure?
  14. What does r2 measure?
  15. State the formal assumptions of regression analysis.
  16. In the prediction equation, , what are the terms.
For students in agriculture and environmental fields.

Air with varying concentrations of CO2 is passed over wheat leaves at a temperature of 35C and uptake of CO2 by the leaves is measured. Three replications are choosen at each of four levels of CO2 . Uptake values (y) for different concentrations (x) are obtained and are as follows:



Concentration(x)   Uptake(y)
75                    .30
75                    .11    
75                    .46
100                   .65
100                   .53 
100                   .71
125                   .89 
125                   .81 
125                  1.02  
150                  1.20
150                  1.81 
150                   .97

  1. Plot the sample data in a scatter diagram. By eye, add in the line you think would fit the data best.
  2. Estimate the parameters in the model and then draw the fitted line onto your scatterplot.
  3. Calculate the Analysis of Variance table and test the null hypotheses of no significant regression. Use
  4. Calculate the value of the t statistic for testing . Use . Show that .
  5. Calculate the sum of squares due to pure experimental error and lack of fit and write the associated ANOVA table. Conduct a test for lack of fit of the linear regression model. Does the linear regression model fit the data well.
  6. Calculate the variance of both and compute the associated 95% confidence intervals.
  7. Using the estimated model, predict the values of y when =90 and =150. Find the 95% prediction intervals for .
For students in engineering fields.

 

 

For students in toxicology and health science fields.

An experiment is run to measure the cholesterol levels on 12 cardiac patients before and after a four-month program of cardiac rehabilitation. For each patient, a reading was taken soon after diagnosis (x) and another was taken after a four-month program of cardiac rehabilitation (y). Three patient were choosen at each of four levels of x. The cholesterol levels obtained were as follows.



pretreatment_level (x)   posttreatment_level (y) 
180                               153
180                               146
180                               175
200                               189
200                               198
200                               195   
220                               209
220                               206
220                               216
240                               182
240                               200
240                               219


  1. Plot the sample data in a scatter diagram. By eye, add in the line you think fits the data best.
  2. Estimate the parameters in the model and then draw the fitted line onto your scatterplot.
  3. Calculate the Analysis of Variance table and test the null hypotheses of no significant regression. Use
  4. Location the value of the t statistics for testing . Use . Show that .
  5. Calculate the sum of squares due to pure experimental error and lack of fit and write the Anova table. Conduct a test for lack of fit of the linear regression model. Does the linear regression model fit the data well?
  6. Calculate the variance of , compute the 95% confidence intervals for .
  7. Use the estimated model, predict the values of y when =210 and =260. Find the 95% confidence intervals for .
For students in community development, education and social services fields.