Living Wage in London - Essay Example

Due: PART A: Descriptive Statistics You are a researcher interested in exploring support for the proposed “living wage” in London. You conduct a small survey and randomly ask 15 Londoners to rate their level of support for the “living wage” on a scale from 0 to 100, with 0 indicating complete opposition, 50 indicating neither opposition nor support, and 100 indicating complete support. You get the following scores: 100, 60, 50, 75, 75, 25, 50, 100, 80, 0, 100, 40, 95, 65, 85 i) Find the 95% and 99% confidence intervals around the mean. Be sure to show your work. SOLUTION Given the scores 100, 60, 50, 75, 75, 25, 50, 100, 80, 0, 100, 40, 95, 65, 85 We first compute the mean Mean, Standard deviation Since the sample size, n |t|) = 0.0000 Pr(T > t) = 1.0000 From the above table, it can be observed that there is a significant difference in the feminist’s feelings between the male and the females (gender). In this case unequal variances are assumed that is, the male and female have different variances as far as feminists’ feelings are concerned. Female respondents were established to possess more feeling on feminists as compared to their male counterparts. For instance, male respondents had an average of 52.707222 feeling towards feminists against 59.56906 of the female respondents. Is there a statistically significant difference between mean warmth towards feminists (fem1) and hclinton? The answer here is yes. This can be answered from the table below which compares the mean warmth toward feminists (0=not warm towards the feminists and 1=warm towards feminists) and the hclinton. In this case, the p-value=0.0000 0 Pr(T < t) = 0.0000 Pr(T > t) = 0.0000 Pr(T > t) = 1.0000 Is there a statistically significant difference between mean warmth towards feminists (fem1) and conservatives? From the Stata output generated it can be seen that unlike for the hclinton there is no significant difference in the mean warmth feeling towards the feminists and conservatives; ttest conservatives, by(fem1) unequal Two-sample t test with unequal variances ------------------------------------------------------------------------------ Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- 0 | 521 60.36276 .8255312 18.8431 58.74098 61.98455 1 | 479 60.58664 1.031776 22.58152 58.55926 62.61402 ---------+-------------------------------------------------------------------- combined | 1000 60.47 .6548419 20.70792 59.18498 61.75502 ---------+-------------------------------------------------------------------- diff | -.2238749 1.321387 -2.817106 2.369356 ------------------------------------------------------------------------------ diff = mean(0) - mean(1) t = -0.1694 Ho: diff = 0 Satterthwaites degrees of freedom = 934.031 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.4327 Pr(|T| > |t|) = 0.8655 Pr(T > t) = 0.5673 PART C: Linear Regression Running regression analysis of . regress polinterest income age educ gender socialclass married Source | SS df MS Number of obs = 61303 -------------+------------------------------ F( 6, 61296) = 594.27 Model | 2271.62132 6 378.603553 Prob > F = 0.0000 Residual | 39051.1916 61296 .637092005 R-squared = 0.0550 -------------+------------------------------ Adj R-squared = 0.0549 Total | 41322.8129 61302 .674085884 Root MSE = .79818 ------------------------------------------------------------------------------ polinterest | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- income | -.0371993 .0018907 -19.67 0.000 -.0409051 -.0334934 age | -.008771 .0002589 -33.88 0.000 -.0092785 -.0082636 educ | -.0437823 .0018244 -24.00 0.000 -.047358 -.0402065 gender | .1537194 .0064682 23.77 0.000 .1410416 .1663971 socialclass | .0399913 .0045668 8.76 0.000 .0310403 .0489423 married | -.0191935 .0071978 -2.67 0.008 -.0333011 -.0050859 _cons | 3.350811 .0301235 111.24 0.000 3.291769 3.409853 ------------------------------------------------------------------------------  income -  The t test statistic for the predictor income is (-0.0371993 /0.0018907) = -19.67 with an associated p-value of 0.000. If we set our alpha level to 0.05, we would reject the null hypothesis and conclude that the regression coefficient for income has been found to be statistically different from zero given age, educ, gender, socialclass and married are in the model. age-  The t test statistic for the predictor age is (-0.008771 /0.0002589) = -33.88 with an associated p-value of 0.000. If we set our alpha level to 0.05, we would reject the null hypothesis and conclude that the regression coefficient for age has been found to be statistically different from zero given income, educ, gender, socialclass and married are in the model. educ -  The t test statistic for the predictor income is (-0.0437823 /0.0018244) = -24.00 with an associated p-value of 0.000. If we set our alpha level to 0.05, we would reject the null hypothesis and conclude that the regression coefficient for income has been found to be statistically different from zero given age, income, gender, socialclass and married are in the model. Similarly trends are recorded for gender, socialclass and married in the model. Checking for multicollinearity Multicollinearity is a condition where independent variables are strongly correlated with each other. The estimates for a regression model cannot be uniquely computed when there is a perfect linear relationship among the predictors. We use VIF command to check for multicollineairty. VIF basically stands for variance inflation factor. As a rule a variable with VIF greater than 10 may open doors for further investigation. From the table below the VIF looks fine implying that there is no need for further investigation since there is no any single variable whose VIF surpasses 10. . vif Variable | VIF 1/VIF -------------+---------------------- income | 1.53 0.652286 age | 1.50 0.664457 socialclass | 1.50 0.667830 educ | 1.48 0.675469 married | 1.19 0.839202 gender | 1.01 0.993604 -------------+---------------------- Mean VIF | 1.37 Checking heteroskedasticity hettest Breusch-Pagan / Cook-Weisberg test for heteroskedasticity Ho: Constant variance Variables: fitted values of polinterest chi2(1) = 4.14 Prob > chi2 = 0.0419 From the above test, prob>chi2=0.0419 chi2 = 0.0000 Log likelihood = -34961.576 Pseudo R2 = 0.0295 trustworthy Coef. Std. Err. z P>z [95% Conf. Interval] age .1382322 .0038341 36.05 0.000 .1307174 .1457469 sex .0597116 .0126445 4.72 0.000 .0349289 .0844943 educ .0023366 .0065937 0.35 0.723 -.0105869 .0152601 region -.0227041 .0193552 -1.17 0.241 -.0606395 .0152313 friend -.2491017 .0095832 -25.99 0.000 -.2678844 -.230319 _cons -.2867207 .0337544 -8.49 0.000 -.3528782 -.2205633 Interpretations age- The coefficient of age is 0.1382322.  This means that an increase in AGE increases the predicted probability of trust.  sex - The coefficient of sex is 0.0591. This means interviewing more female respondents increases the predicted probability of trust.  educ - The coefficient of educ is 0.023366.  This means that an increase in EDUCATION Level increases the predicted probability of trust.  region - The coefficient of region is -0.227.  This means that an increase in some of the regions in the study decreases the predicted probability of trust.  friend - The coefficient of friend is -0.2491017.  This means that an increase in friends whose friendship level is low decreases the predicted probability of trust.     _cons - The constant term is -0.2867207.  This means that if all of the predictors (age, sex, educ, region and friend) are evaluated at zero, the predicted probability of trust is F(-2.797884) . So, as expected, the predicted probability of a person with AGE zero and a GPA of zero has an extremely low predicted probability of trust. To generate values from F in Stata, use the normal function. For example,  age -  The z test statistic for the predictor age is (.1382322 /.0038341/) = 36.05 with an associated p-value of 0.000. If we set our alpha level to 0.05, we would reject the null hypothesis and conclude that the regression coefficient for age has been found to be statistically different from zero given sex, friend, region and educ are in the model.  sex - The z test statistic for the predictor sex is (.0597116/.0065937) = 4.72 with an associated p-value of 0.000. If we set our alpha level to 0.05, we would reject the null hypothesis and conclude that the regression coefficient for sex has been found to be statistically different from zero given age, friend, region and educ are in the model.  educ - The z test statistic for the predictor educ is (.0023366/.0126445) = 0.35 with an associated p-value of 0.723 If we set our alpha level to 0.05, we would not reject the null hypothesis and conclude that the regression coefficient for educ has not been found to be statistically different from zero given sex, friend, region and age are in the model. Marginal effects following the probit model . dprobit trustworthy age sex educ region friend Iteration 0: log likelihood = -36022.46 Iteration 1: log likelihood = -34963.084 Iteration 2: log likelihood = -34961.576 Iteration 3: log likelihood = -34961.576 Probit regression, reporting marginal effects Number of obs = 55161 LR chi2(5) =2121.77 Prob > chi2 = 0.0000 Log likelihood = -34961.576 Pseudo R2 = 0.0295 trustw~y dF/dx Std. Err. z P>z x-bar [ 95% C.I. ] age .0514657 .0014268 36.05 0.000 1.62829 .048669 .054262 sex .0222314 .0047077 4.72 0.000 1.73269 .013005 .031458 educ .0008699 .002455 0.35 0.723 .665234 -.003942 .005682 region -.008453 .0072062 -1.17 0.241 1.08515 -.022577 .005671 friend -.0927439 .0035637 -25.99 0.000 1.56739 -.099729 -.085759 obs. P .3593481 pred. P .3550579 (at x-bar) z and P>z correspond to the test of the underlying coefficient being 0 Interpretations Age- dF/dx=0.514657 implying that a unit change in age results to an increase in trust level by a factor close to 0.514657. Sex- dF/dx=0.222314 implying that a unit change in say increase in the number of female results to an increase in trust level by a factor close to 0.222314. educ- dF/dx=0.0008699 implying that a unit change in say increase in the level of education results to an increase in trust level by a factor close to 0.0008699. Difference between logit and probit Logit and probit differ in how they define (f*). The logit uses the cumulative distribution function of the logistic distribution while the probit model uses cumulative distribution function of the standard normal distribution. Both logit and probit functions takes any number and rescales them to fall between 0 and 1. Both methods will yield similar (though not identical) inferences. PART E: Regression Interpretation 2) Model on the recent MPs’ expenses scandal The probability of MP retiring was established to be dependent on; Medianamed- the coefficient is 0.113 implying that an increase in the media naming would result to an increase in the chances of MP stepping down before 2010 general elections (retiring) by factor 0.113 Repaid- the coefficient is 0.00005 implying that an increase in the repayment of the MP would subsequently increase the chances of retiring before 2010 general elections by 0.00005. 05majority-the coefficient in this case is -0.0007, this indicates that having an increase in the 05majority would actually reduce the chances of an MP retiring before 2010 general elections. Labour-has a coefficient of 0.107, indicating that an increase in the labour chances had a positive relation in MP retiring before 2010 general elections by a factor close to 0.107 Status-the coefficient is -0.019, an increase in status level would reduce the probability of an MP stepping down before 2010 general election by 0.019 Seniority-with a coefficient of 0.08, this indicates that the more senior the MP is, the chances of him or her stepping down increases by 0.08 Age-coefficient of 0.011, indicating that the more aged MPs stood a better chance of retiring before 2010 general election by a factor of 0.011 Female-with a coefficient of 0.037, as the chances of an MP gears towards being a female so does the chances of retiring before 2010 general elections. Read More