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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.Suppose that you wish to estimate the effect of class attendance on student performance. A basic model is examscore = β0 + β1attendance + β2priorGP A + u where examscore is students’ score on the exam (from 1 to 6), attendance is the number of TA sessions attended on Zoom (from 0 to 9), and priorGPA is the average exam grade last year. (a) Let internet be the quality of internet at the student’s study place. Do you think internet satisfies the independence assumption? What about the exclusion restriction? (b) Assuming that internet satisfies the conditions above, what other condition must internet satisfy in order to be a valid IV for attendance? (c) Suppose, we add the interaction term priorGP A × attendance. Interpret the coefficient on the interaction term. (d) (Difficult) If attendance is endogenous, then, in general, so is priorGP A × attendance. What might be a good IV for priorGP A × attendance?Chlorophylls a and b are plant pigments that absorb sunlight and transfer the energy into photosynthesis of carbohydrates from CO2 and H2O, releasing O2 in the process. Chlorophylls were extracted from chopped up grass and measured by spectrophotometry. The table shows results for chlorophyll a for four separate analysis of five blades of grass. Chlorophyll a (g/L) Blade 1 Blade 2 Blade 3 Blade 4 Blade 5 1.09 1.26 1.1 1.23 0.85 0.86 0.96 1.21 1.3 0.65 0.93 0.8 1.27 0.97 0.86 0.99 0.73 1.12 0.97 1.03 Four replicate measurements for each blade of grass tell us the precision of the analytical procedure (sanalysis). Differences between mean values for each of the five blades of grass are a measure of variation due to sampling (ssampling). Using Excel and it’s ANOVA function, find the standard deviations attributable to sampling and to analysis, as well as the overall standard deviation arising from both sources.
- The following model was specified to investigate the relationship between mineral exploitation and energy consumption in a small state over 1970-2006: ln(mining)t= β0 + β1ln(GDP_m)t + β2ln(exports)t + β3ln(energy)t + et where mining = the output of the mining and quarrying industry (constant 2000 US dollars); GDP_m = GDP less mining and quarrying industrial output (constant 2000 US dollars); exports = exports (constant 2000 US dollars); and energy = energy consumption (million kilowatts hours). OLS estimation of the preceding equation yields ln(mining)t=-5.76+0.81ln(GDP_m)t+0.21ln(exports)t-0.09ln(energy)t t-stat = (-3.82) (12.76) (3.53) (-2.49) p-value = (0.001) (0.000) (0.001) (0.017) R2=0.8905 n = 37 Durbin-Watson stat = 0.98 d) Interpret the coefficient on ln(energy). e) Are coefficients’ signs on explanatory variables within your expectation? Answer this question with a…The following model was specified to investigate the relationship between mineral exploitation and energy consumption in a small state over 1970-2006: ln(mining)t= β0 + β1ln(GDP_m)t + β2ln(exports)t + β3ln(energy)t + et where mining = the output of the mining and quarrying industry (constant 2000 US dollars); GDP_m = GDP less mining and quarrying industrial output (constant 2000 US dollars); exports = exports (constant 2000 US dollars); and energy = energy consumption (million kilowatts hours). OLS estimation of the preceding equation yields ln(mining)t=-5.76+0.81ln(GDP_m)t+0.21ln(exports)t-0.09ln(energy)t t-stat = (-3.82) (12.76) (3.53) (-2.49) p-value = (0.001) (0.000) (0.001) (0.017) R2=0.8905 n = 37 Durbin-Watson stat = 0.98 a) Use the p value approach to find out whether energy contributes negatively to mineral exploitation at the 5% level. Hint: specify the 5+1 steps. b)…The number of murders and robberies per 100,000 population for a random selection of states are shown. Find the equation of the regression line y'=ax+b, and predict the number of robberies when x=4.5 murders murders,x: 2.4,2.7,5.6,2.6,2.1,3.3,6.6,5.7 robberies,y : 25.3,14.3,151.6,91.1,80,49,17.3,45.8
- The coefficients in a distributed lag regression of Y on X and its lags can be interpreted as the dynamic causal effects when the time path of X is determined randomly and independently of other factors that influence Y. Explain How?Consider a model with an interaction term between being female and being married. The dependent variable is the log of the hourly wage: log(wage) = 0.151 - 0.038 female + 0.1 married - 0.301 female* married + 0.079 educ + 0.027 exper+0.029 tenure (0.072) (0.056) (0.055) (0.007) (0.005) (0.007) n = 536, R2 = 0.461 Numbers in parantheses are standard errors of coefficients. Given the estimation result and the observation number fill in the blanks below which aim at discussing the statistical significance of variables. The test statistic of the interaction term is The critical value at 1% significance level is Then the interaction term statistically significant at 1% significance level. (Hint: to fill the blank make a choice between "is" and "is not".)Construct the simple linear regression equation of Y on X if n = 7, x,=113, E Ey-182 and Exy, =3186. =1983,
- A public health researcher is investigating the effectiveness of fluoride in preventing cavities. Two communities are studied, one with a fluoridiated water supply and the second with non-fluoridated water. A random sample of n1 = found that Y1 400 and n2 = = 348 residents in the first community and y2 900 residents are obtained from these two communities, respectively. It was 819 residents in the second community had cavities. Consider modeling these counts by two binomial distributions with the probability of success (presence of cavities) as 71 and 72 for communities with fluoridated and non-fluoridated water supplies, respectively. (i.e. consider the random variables Y Bin(n1, T1) and Y2 ~ Bin(n2, T2).) a. Let P = Y1/n1 and P2 with cavities in each population. Approximate the sampling distributions of P1 and P2. b. Based on your answer from (a), approximate the sampling distribution for the difference in sample proportions, D = P1 – P2. (Hint: think of this as a sum of normal…consider the regression model Yi = β0 + β1Xi +ui. suppose you know that β0 = 0. derive a formula for the least square estimator of β1X X zy Section 5.4- QNT/275T: Statistics x + 598163/chapter/5/section/4 for Decision Making home > nce between two population means 4.1: Hypothesis test for the difference between two population means. Jump to level 1 A clinical researcher performs a clinical trial on 14 patients to determine whether a drug treatment has an effect on serum glucose. The sample mean glucose of the patients before and after the treatment are summarized in the following table. The sample standard deviation of the differences was 8. Before treatment What is the test statistic? Ex: 0.123 Check What type of hypothesis test should be performed? Select Select Left-tailed z-test Paired t-test Two-tailed z-test Unpaired t-test Next After treatment 75 Sample mean glucose (mg/dL) What is the number of degrees of freedom? Ex: 25 Does sufficient evidence exist to support the claim that the drug treatment has an effect on serum glucose at the a = 0.05 significance level? Select 81 MESA 81101 2 hp 3 I
