1. Why do some students carry weapons inside and outside of school? Who are those students? Dr. Smartypants is at it again: He is wondering if perhaps students who are bullied are the ones who are most prone to carrying weapons. To study this, he asks to you run a regression model with two indicators of if the student had been bullied on or offline. He hypothesizes that offline bullying is more likely to cause weapon carrying since it is in person. In his theory, offline bullying is unlikely to have an effect: a. What are your null and research hypotheses? Be sure to include hypotheses for both independent variables and your regression model F test. b. Multiple Regression in SPSS: As with single-variable regression, begin by selecting analyze-regression-linear. Place the variable Weaponcarrying in the dependent variable spot and both qn24 and qn25 in the independent variable slot. That's it! Select ok. You'll notice that the output is all but identical to the output provided within this chapter's text! c. Use this output to answer the following: i. What proportion of the variation in the weapon carrying scale is explained by these two variables? ii. What do the slope coefficients for each tell us? Recall that these are binary indicators, so a one-unit change in this case reflects the difference between not bullied and bullied students. The hypothesis tests? iii. How do you interpret the Intercept in this case? iv. ls Dr. Smartypants's theory supported by these results? 2. Dr. Smartypants says he'd like to contro! for some additional variables to minimize the risk of confounding. In particular, he wants to control for student age, being male, year in school, and if the student is white versus nonwhite. To do this, include the variables age, sex, white, and grade in the model: a. Does this change your results or conclusions? b. How has your model R-squared changed? c. Do you find any interesting or new effects in the independent variables you have added? d. Take a look at the column called \"standardized coefficients.\" These are your beta weights. What coefficients have the strongest effect on the dependent variable? e. Briefly summarize your results for Dr. Smartypants. Are there any confounders or concerns that need to be considered? 3. You decide to check if multicollinearity may be an issue for your analysis. One simple way to look at this is to see if your independent variables are strongly correlated with one another. Consider a correlation coefficient of .7 to be evidence of multicollinearity in this case: a. Do you find any evidence of multicollinearity? If so, explain why those two variables might be collinear. b. If multicollinearity was found, reestimate your multiple regression model with one of the problem variables removed. Have your substantive conclusions changed? 4. You realize there is a potential confounder at play here. Maybe instead of bullying being the \"cause\" of weapon use, it's actually a sense of fear and hostility in the school? If a person gets bullied, they might get in fights or just feel unsafe. Perhaps it is students who are exposed to a great deal of conflict and hostility that are carrying weapons? Let's make sure the bullying effects are still present after controlling for that confounder! a. Estimate your multiple regression model with the bullying variables, age, sex, grade and white. This time also add the variable Hostileenvironment. b. Have your results (not) changed? Does this model fit better than earlier models? What is your strongest effect in the model, based on your standardized coefficients and f statistics? c. Write a memo to Dr. Smartypants that uses the results of this model to either support or critique his theory presented in question 1. Be sure to include your model R-squared and how it has/hasn't changed, what happens when you control for the confounder, and the \"why\" that explains why the variables are related to the dependent variable. d. If you were tasked with developing an intervention to prevent weapon carrying in school, what would you recommend? What should be prioritized? e. Have you met the criteria for causality in this final model? If no, what more must be done