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PPA 207: Quantitative Methods Meeting 8, Spring 2004 1. Homework Studenmund, Chapter 7, Number 13 a. The dependent variable (E) is the defined as the efficiency rate or total output to goal output. The explanatory variables are total output (Q), absentee rate in percentage (A), and incidents of violence (V). I hypothesize that Q should have a positive influence on E. A and V should both have a negative influence on E. The dof are 20 and using a 95 percent level of confidence the critical t in a one-tailed test is 1.725; in a two-tailed test it is 2.086. The calculated t on Q is 4.0; on A it is 2.0 and on V it is 0.125.Therefore we can "accept" the alternative hypothesis that Q has a positive influence on E using both the one-tailed and two-tailed test (actual t > critical t). We can also "accept" the alternative hypothesis that A has a negative influence on E if using one-tailed test, but not if using a two-tailed test. We cannot "accept" the alternative hypothesis that V has a negative influence on E using either a one or two tailed test. b. The calculated effect of Q on E is done with both in log form. Thus the regression coefficient of 0.16 represents the percentage change in E given a one-percent change in Q. We have calculated an elasticity that is constant for all values of E. With regards to A and V they are not in log form. The regression coefficient of -0.020 on A and -0.0001 on V are not elasticities but need to multiplied by a value of either A or V to transform them into an elasticity. Usually this value is chosen as the mean. Thus the elasticity is not constant, but varies by the chosen value for either A or V. c. As stated in part a, we cannot reject the null hypothesis that V has a zero or positive effect on E. Thus the court cannot conclude from this regression that violence had a significant impact on efficiency rate. d. There are obviously omitted variable problems. There are other important variables that determine efficiency rate that have been left out of this regression. This may be the reason for the finding that V has no effect on E. There is also a problem with taking the log of E and the log of Q and creating a log-log functional form. Since E equals Q over goal output, and in a given week goal output is constant, a one unit increase in Q will result in a constant increase in E. For example assume that goal output is 3. If Q equals 1, E equals 1/3; if Q equals 2, E equals 2/3; if Q equals 3, E equals 3/3; etc. For each one unit increase in Q, E increases by 1/3. This is a pure linear relationship and there is no reason to run a regression that models it as a non-linear relationship. So the one thing that I would change is drop taking the log of Q and just re-run as a left log-linear regression. Pollock, Chapter 5, Numbers 1 and 2 2. Midterm Exam 3. Pollock, Chapter 6, Making Inferences About Sample Means Draw a sample that wish to make inferences about entire population on Need to discuss “confidence” or “probability” of being correct For example, calculate mean How confident that it is representative of population Load NES2000.sav Descriptive statistics on SPEND13 How confident can you be in mean Based upon calculated standard error One-Sample T Test (95% confidence interval) Analyze=>compare means=> one-sample T test Lower and upper bounds reported Can change it to represent a 90% confidence interval Hypothesize that political science majors are more likely to favor gov’t spending The mean value of SPEND13 = 5.86 (total sample mean = 5.76) Within confidence intervals calculated earlier Run another one-sample T test, but enter 5.86 into test value box Sig. in two tailed is 0.134 (or 0.067 in each tail) Meaning that there is a 6.7% probability of observing this difference if means of two groups are the same We seek less than 5% probability Compare the sample means of a dependent variable for two groups Analyze=>compare means=>independent sample T tests Need test variables, grouping variable (define groups) Means reported for each variable, by male and female Mean differences are reported below Check Levene’s test for equality of variances Value greater than or equal to 0.5, use equal variances assumed Look at sig. (2-tailed) and divide by two 15.9% of time we could observe difference even if same Cannot reject null hypothesis that same Not the case for opinion on women’s movement 5. Homework Due the Start of Meeting Nine (1) Read all of the material under meeting nine in the syllabus; come prepared to discuss. (2) A typed and well developed question from reading assignment for week nine. (3) Answer questions 1, 2 and 3 in Pollock, Chapter 6, handwritten on given pages and turn in any requested SPSS output.