1. Two sociologists collected the data found in the document entitled DI IQ.dat which contains the IQ and delinquency index (DI) of 18 inmates. The IQ score is the result from a traditional WISC IQ test and the DI score measures both accounts for both the number and severity of the crimes that were committed by a particular inmate and ranges from zero to fifty. Researchers believe that delinquency is dependent on IQ.

1. Construct the appropriate scatterplot. What do you notice? Is SLR appropriate?
2. Fit the appropriate SLR model. Report the prediction equation and the coefficient of determination. Are you surprised by how low the coefficient of determination is? Why or why not?
3. Researchers have determined that there was an error when collecting the data from one inmate. Based on your plot and any relevant information from fitting the SLR, which inmate’s data most likely contains the error?
4. Remove the anomalous observation and refit the SLR model. What are the prediction equation and coefficient of determination now? Does this more accurately reflect the true relationship in the data? Why or why not?
5. Check to see if the assumptions are violated for the model you found in 1d.
6. Using the model you found in 1d interpret the regression coefficients in context.
7. Construct a 95% CI for the true slope parameter. Be sure to interpret.

2. A researcher is interested in studying the habitat of bog turtles in Virginia. The data found in the file bog turtle. dat contains a response variable and three explanatory variables. Each sampling unit is a wetland in southwestern Virginia approximately 1 hectare in size. Within each wetland the response (a measure of habitat sustainability) and the explanatory variables (measuring environmental conditions such as soil granularity, percent litter, percent open water, percent bare soil, percent woody vegetation, etc.) were measured. Note that we are not told what three variables are provided here.

1. Create a correlation matrix. Which of the regressors is most strongly associated with the response? Which the least?
2. Create a scatterplot matrix. Does the scatterplot matrix support your answer to 2a?
3. Based on your answers to 2a and 2b how many variables do you think should be included in the final model? Which one(s)?
4. Fit the full model that includes all three regressors. Report the model equation and the multiple coefficient of determination.
5. Starting only with SSR and SST show how you would compute the ANOVA table if MINITAB had not been available and those were the only two quantities you had been given.

6. 2

   Are the set of regressors independent of the response? Is it useful for predictions? Provide a statistic that justifies each of your answers.

1. Is there a variable that you think should be removed from the model? Which one? Provide justification for its removal.
2. Refit the model with this variable removed. Report the model equation and the multiple coefficient of determination. Do you feel this model is as good as the model containing all the regressors? Why or why not?
3. Interpret the model coefficients from the two variable model with as much context as possible.
4. Obtain a 95% CI and PI for the scenario when X 1 = 700, X 2 = 25 and X 3 = 8.

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