Econometrics Assessment Answer

Problem Set 3
Time Series and Autocorrelation
EC421 Introduction to Econometrics

Problem 1

PtGas 01PtoiluNo, we cant expect OLS estimator to be consistent. From the history, it is evident that gas price depends on previous periods gas prices. So, there can be autocorrelation problem.
OLS estimate of model 1a is provided below
Call
lm(formula price_gas price_oil, data data)
Residuals
Min 1Q Median 3Q Max
-3.4760 -1.4466 -0.8046 1.4670 9.0623

Coefficients

Estimate Std. Error t value Pr(gtt)
(Intercept) 3.336013 0.263876 12.642 lt 2e-16
price_oil 0.017453 0.003956 4.412 1.5e-05
—
Signif. codes 0 0.001 0.01 0.05 . 0.1 1
Residual standard error 2.118 on 263 degrees of freedom
Multiple R-squared 0.06891,Adjusted R-squared 0.06537
F-statistic 19.46 on 1 and 263 DF, p-value 1.497e-05
1 0.01745
p-value 0.0000

Coefficient of average price of oil, per barrel comes out 0.01745, which is positive. This means that there is 0.01745 increase in the average price of natural gas, per 1MM BTU for every 1 increase in the average price of oil, per barrel. In Economics, statistical significance is seen by the p-value. P-value for coefficient 1 is 0.000, which implies that we can reject the null hypothesis of non-significance even at 1 percent significance level. Therefore, coefficient 1 is significant at 1 percent significance level.
Significance of 1 doesnt imply that price of oil explains lot of variation in the price of natural gas. R-sq explains, how much variation in the price of natural gas can be explained by price of oil.

R-sq 0.06891
Only 6.89 percent variation in the price of natural gas can be explained by price of oil.
Now, consider the following model
PtGas 01Ptoil2Pt-1oil3Pt-2oilutOLS estimate of the model is as
Residuals
Min 1Q Median 3Q Max
-3.4767 -1.4734 -0.8187 1.4493 9.1105

Coefficients
Estimate Std. Error t value Pr(gtt)
(Intercept) 3.373472 0.268789 12.551 lt2e-16
price_oil 0.026040 0.026720 0.975 0.331
lag(price_oil, 1) 0.002325 0.043720 0.053 0.958
lag(price_oil, 2) -0.011482 0.026651 -0.431 0.667
—
Signif. codes 0 0.001 0.01 0.05 . 0.1 1
Residual standard error 2.131 on 259 degrees of freedom
(2 observations deleted due to missingness)
Multiple R-squared 0.0684,Adjusted R-squared 0.05761
F-statistic 6.339 on 3 and 259 DF, p-value 0.0003663
For Model 1a For Model 1d
1 0.01745 10.0260 p- value 0.000 P-value 0.331

The coefficient of natural price of oil is 0.026 for new model, which is greater than the coefficient we got for model 1a. But coefficient 1 is not significant at 5 percent significance level as the p-value is greater than 0.05. Therefore, natural price of oil affects natural price of gas positively but not significantly.
20.0023253-0.011482Oil price of previous month has positive but not significant impact on current natural price of gas whereas Oil price of previous to previous month has negative impact on natural price of gas. So, there is 0.00232 increase in the current price of natural gas for every 1 increase in the previous months oil price, and there is -0.011482 decrease in the current price of natural gas for every 1 increase in the previous to previous months oil price. 2 and 3 are insignificant at 5 percent significance level as the p-values are greater than 0.05.
R-sq is almost same for both the models. Though, there is notable difference between adjusted R- squared of both the models. Adjusted R-sq for model used in 1d is slightly lesser than the adjusted R-sq for model used in 1a. So, lag terms dont improve the model more than expected by chance.

A Wald test is used to compare the models used in 1a and 1d.

Wald test
Model 1 price_gas price_oil lag(price_oil, 1) lag(price_oil, 2)
Model 2 price_gas price_oilRes.Df Df F Pr(gtF)
1 259
2 261 -2 0.2342 0.7914P-value for Wald test is 0.7914, which implies that we have to accept the null hypothesis. So, adding the lag terms doesnt significantly improve the model.

No, we cant expect the OLS to be consistent for 1. From the history, it is evident that gas price depends on previous periods gas prices. So, there can be autocorrelation problem. OLS estimator are inconsistent in the presence of autocorrelation.
Now, consider the following model
PtGas 01Ptoil2Pt-1oil3Pt-1GasuOLS Estimate of the model
Residuals
Min 1Q Median 3Q Max
-3.9702 -0.3490 -0.0746 0.2350 3.6602
Coefficients
Estimate Std. Error t value Pr(gtt)
(Intercept) 0.219682 0.117673 1.867 0.06304 .
price_oil 0.026277 0.008660 3.034 0.00265
lag(price_oil, 1) -0.025445 0.008645 -2.943 0.00354
lag(price_gas, 1) 0.937327 0.021633 43.328 lt 2e-16
—
Signif. codes 0 0.001 0.01 0.05 . 0.1 1
Residual standard error 0.7427 on 260 degrees of freedom
(1 observation deleted due to missingness)
Multiple R-squared 0.8868,Adjusted R-squared 0.8855
F-statistic 679 on 3 and 260 DF, p-value lt 2.2e-16

1 0.026277, 3 0.937327For model used in 1i, estimate of 1 is highest among the estimates of 1 for all the three models. Estimate of 1 is significant at 5 percent significance level as the p-value (0.026) is less than 0.05. Therefore, natural price of oil affects natural price of gas positively and significantly.
Gas price of previous month has positive and significant impact on current months natural price of gas. There is 0.937327 increase in the current price of natural gas for every 1 increase in the previous months gas price.
R-sq for model used in 1i, is significantly higher than the R-sq of previous models. Now, 88.68 percent variation in the natural price of gas can be explained by the model used in 1i. Therefore, it can be said that, there is autocorrelation in the model.

Problem 2

Autocorrelation has impact on biasedness and consistency of OLS estimates of model used in 1a and 1d. OLS estimates becomes inconsistent due to autocorrelation. OLS estimates are not BLUE anymore. While OLS estimates of model used in 1i are consistent but unbiased.
See the code
Residual plot over the months and ACF plot over the lag is shown below

Residual plot does not show any particular pattern. Autocorrelation function plot over the lags is shown below. On the graph, there is vertical line corresponding to each lag. The height of each spike shows the corresponding value of autocorrelation function. For 1i model, value of the autocorrelation function is close to zero for all the lags and most of the spikes are not significant. This means there is no autocorrelation in the model.

For model 1a and 1d, Residual plot over the months and ACF plot over the lag is shown below

Autocorrelation plot shows that most of the spikes are statistically significant. So, there is autocorrelation problem in the model. Residual plot also shows a particular pattern.

Autocorrelation plots for model 1a and 1d show that most of the spikes are statistically significant. So, there is autocorrelation problem in the models. Residual plot also shows a particular pattern. Model 1a and model 1d doesnt include gas price of previous month while from the above analysis, it is evident that gas price of previous month has significant impact on the current months gas price. R-sq also significantly improved by adding the previous months gas price.
If error term in not autocorrelated then we can expect OLS estimates to be consistent but biased.
E(), plim P-value is less than 0.05, which means that there is second order autocorrelation in the model.
Res.Df Df F Pr(gtF) 1 260
2 261 -1 8.6624 0.003542
—
Signif. codes 0 0.001 0.01 0.05 . 0.1 1
No, we wont interpret our estimates as casual. Now, (12) combinedly shows the impact of oil price on natural price of gas instead of 1.

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"

Clinical Nursing Assessment Answer

Question 1:

In the given case study, patient Jon had the complication of angina. According to Akbas et al. (2019), angina pectoris is medical condition that has been characterized by severe pain in the chest due to the inadequate flow of blood to the muscles of heart. The various causes behind the progression of angina are building of the fatty substances in the arteries (Bentzon, Otsuka, Virmani & Falk, 2014). These substances are known as plaques and development of plaques in the artery leads to blockage in the flow of blood to muscles of heart.  The increase in the force and increased exercise of heart muscles leads to angina (Bentzon et al., 2014).  The main pathophysiology behind the progression of angina includes a myocardial imbalance between oxygen demand and supply.  This imbalance leads to transition from aerobic metabolism to anaerobic metabolism in myocardial cells which results in the alterations of mechanical and electrical functionality of myocardial cells (Ford, Corcoran, & Berry, 2018).  The main mediator of angina pain is adenosine (Iqbal et al., 2016). The process of degradation of adenosine triphosphate and its diffusion in the extracellular space resulted in the dilation of arteries and consequently lead to pain in chest (Iqbal et al., 2016). The stimulation of A1 receptors in the cardiac afferent nerve endings leads to adenosine-mediated angina (Iqbal et al., 2016). The elevation in the heart rate and myocardial contraction leads to enhanced oxygen demand and failure to mitigate this demand results in the progression of angina (Ford et al., 2018). It has been reported in the case study that the patient has the medical history of hypercholesterolemia hypertension and angina. Also, he used to smoke 20 cigarettes for 25 years. According to MacKenzie, Greig, Hay and Pemberton (2017),the various risk factors for the progression of angina include family history, diabetes, smoking, obesity, hypercholesterolemia, hypertension and history of CAD.  As these factors are highly prevalent in the patient, adequate preventive pharmacology and preventive strategies are required to be implemented in order to prevent the mortality incident. The various preventive medicines like aspirin, angiotensin convertase enzyme and statins may help in prevention of angina incidents (Institute of Quality and Efficiency in Healthcare, 2013). It has been reported that aspirin is an antiplatelets agent, statins lower the blood cholesterol level and ACE helps in lowering the blood pressure of the patient which are main risk factors behind the progression of angina (Institute of Quality and Efficiency in Healthcare, 2013). According to Boden et al. (2014), the secondary preventions like adequate lifestyle, smoking cessation, healthy diet, exercise, and increased in physical activity helps in the prevention of incidences of angina among the patients.

Question 2:

The physical assessment of the patient has been done in order to analyze the severity of the complication. The physical assessment has been done in order to analyze the probabilities of coronary artery diseases followed angina (Ayerbe et al., 2016).The three physical nursing assessments which would be appropriate for the complaints of Jon are assessment of pain, ECG and physical examination.

Pain assessment: According to Balla, Pavasini and Ferrari (2018), pain is the most common clinical manifestation for angina and it is subjective in nature. It has been reported that there is mysterious relationship between myalgic pain and angina pectoris (Leach & Fisher, 2013). This pain is mainly noticed in muscles of shoulder, trapezius muscles and periscapular muscles (Leach & Fisher, 2013).  The assessment of this pain can help in identification of severity of the complication encountered by the patient because it signals cardiac status of the patient. O’Donovan (2013) stated that pain score, pain scales and visual analogs help on assessment and quantification of chest pain and help in assessment of efficacy of administered treatment.  The main things which need to be measured during pain assessment include location of the pain, tightness, choking, precipitation, duration, onset, radiation, associated features and relieving factors of pain (Ratheesh, Sujatha & Lingappa, 2015).

Electrocardiogram: It is an important nursing assessment tools which is used for the assessment of risk factors and severity of angina pectoris (Vrints, Senior, Crea & Sechtem, 2016).  According to Alaeddini (2018), ECG helps in assessment of various risk factors alike myocardial infarction history, delay in ventricular conduction, atrioventricular blockage, deviation in ST complex or deviation in T wave and arrhythmias. The ECG assessment is used by the nursing professionals to evaluate the incidents and frequency of silent ischemia (Alaeddini, 2018).  It has been reported that silent ischemia is a predictor of death or sever complications in patients have the complication of angina (Alaeddini, 2018).

Physical examination: The physical examination includes inspections, percussion, palpation and auscultation. It has been stated that inspection of the body of the patient helps in examining the presence/absence of cyanosis which can be detected by grey/bluish color of skin (Denn et al., 2017). The examination for palpations showed the tenderness of chest wall, overlying structures or inflammatory process progression.  The evaluation of percussion helps in detecting fluid collection and areas of low air entry (Denn et al., 2017). Auscultations assessment has been done in order to analyze the accessory sounds in the patient during breathing (Denn et al.,2017). The detection of these physical parameters helps in analyzing the severity of complication encountered by Jon.

Question 3:

Nursing interventions:

From the assessment of the patient, it has been found that his pulse was irregular and 110 bpm, respiration rate was 24 and SaO2 was 93% room air. In order to manage the complications of the patient, the three nursing interventions would be treatment of anxiety physiotherapy and healthy diet.

Treatment of anxiety: It has been reported that anxiety is highly associated with the patients having cardiovascular problems (Blumenthal et al., 2016). Anxiety is defined as a feeling of worry or stress (Blumenthal et al., 2016). The fear of losing the life is leads to anxiety among the patients suffering from angina.  It has been reported that the management of anxiety among thee patients having cardiovascular complications is an important nursing intervention which could help in reducing symptoms and enhancing clinical outcomes of the patients (Blumenthal et al.,  2016).The cognitive based therapies for patient education about the relationship between feelings, thoughts, behaviors and enhancing patient awareness about the automatic thoughts is an important intervention which could help in preventing anxiety among the patents (Zetta, Smith, Jones, Allcoat, & Sullivan, 2011).

Physiotherapy: It has been reported that cardiac rehabilitation is an important intervention for the patients who have encountered the complication of angina and other cardiac diseases (Babu, Noone, Narayanan & Franklin, 2012). It is processes during which the continuous monitoring of vitals has been done and patients have been motivate to get engaged in the aerobic activities (Physiopedia, n.d.). According to (Babu et al. (2012), the exercise began with the low level aerobics of lower limbs and upper limbs below an intensity of angina threshold. The Jacobson’s technique could help in relaxing the patient and helps in providing knowledge about the method of management of angina episodes (Babu et al., 2012). This would help in enhancing the ischemic threshold of the patient so that comparatively high levels of exertion can be undertaken by the patient (Babu et al., 2012).

Healthy Diet: It has been reported that good nutrition is very important for the health of heart (MedlinePlus, 2019). Healthy diet helps in managing several risk factors associated with the progression of health diseases like angina.  According to Massera, Graf, Barba and Ostfeld  (2016), plant based diets helps in reduction of low density lipoproteins and cholesterol level in the plasmas. It helps in glycaemic control, weight and plasma lipids reduction in the patients among whom these risk factors are highly prevalent. So, one of the appropriate nursing interventions for Jon would be healthy diet which can control risk factors behind the progression of angina.

Question 4:

Nitroglycerin sublingual tablets have been used to treat the complications of sudden angina attacks (Aroesty & Kannam, 2018). It has been used for the prevention of angina during the engagement of patient in rigorous activities because there are certain activities which maylead to the incidents of angina (MedlinePlus, 2019). It is a class of vasodilators which helps in blood vessels relaxation and reduced the work of heart during angina (MedlinePlus, 2019).

For the administration of nitroglycerin, the tablet needs to be kept under the tongue or in the pouch of the buccal cavity and this drug gets rapidly dissolved and absorbed from here. The effects of sublingual nitroglycerin can be seen within 2-5 minutes and last for 15 to 30 minutes (Aroesty & Kannam, 2018). The tongue should be moist during the administration of the drug and it has been recommended that a glass of water can be taken prior to the administration of drug (Aroesty & Kannam, 2018). The drug can be administered prophylactically 5 to 10 minute before engagement in the rigorous activities which can result in acute angina attacks (RxList, 2019). There are various benefits of using nitroglycerin sublingual tablets. According to Boden, Padala, Cabral, Buschmann and Sidhu (2015), these tablets are short-acting and showtheir effects in 2 to 5 minutes. It can be used as prophylactic agents in the prevention of angina. It is a safe, effective, and convenient medication therapy with multiple benefits. It is known as an exertional drug which is used for the reduction of left ventricular pressure. The various risks that are associated with the use of this drug are increased vasodilatation, venous pooling, hypotension, and low cardiac output (Kim & Schaller, 2018). In addition to it, palpitation, tachycardia, nausea, vomiting, vertigo, confusion, throbbing, visual impairment and fever can be observed in some patients (Kim & Schaller, 2018). The drug is contradicted to the patients who have allergy from this drug, have early complications of severe anemia, myocardial infarction, hypersensitivity to nitroglycerin and using PDE-5 (Golden State Medical Supply, 2017). The various educations that needs to be given to the patient for the safe use of this medicine includes method of administration of the drug that it should be taken as sublingual tablet nor to be chewed or swallowed, potential side effects of the drug, storage information of the drug, repetition of the drug in case of persistent pain and contact to the nurses in case of an emergency (Golden State Medical Supply, 2017).

Question 5

The 12 lead ECG has been used to diagnose the chest discomfort of the patient. In the given ECG strip, there is an abnormality in ST complex. The ST wave is elevated in the given strip of ECG. When the ST elevation has been observed in two consecutive leads, it indicted the incidence of acute ST-segment Elevation Myocardial Infarction (STEMI) (Coppola et al., 2013). It has been reported that in an ECG strip, the records that have been taken at a speed of 25mm/s with amplification of 10mm/mv the measurement of ST segment should be done from the baseline after J point. If the deviation of more than 0.2mV and more than 0.15 mv in males and females respectively observed, it signifies blockage in left bundle branch, left ventricle aneurysm and hypertrophic cardiomyopathy (Coppola et al., 2013). This finding needs to be reported to the doctor immediately because the elevation in the ST segment and myocardial infarction could be life-threatening for Jon.  The early diagnosis of the ailment may prevent the patient from mortality incidents and timely management could be done if the nurse could notify the deteriorating condition of the patient (Said, Bloo, de Nooijer, & Slootweg, 2015).

References

Alaeddini, J. (2018). Angina pectoris. Retrieved fromhttps//emedicine.medscape.com/article/150215-workupc12
Aroesty, J. M., amp Kannam, J. P. (2018). Patient education Chest pain (beyond the basics). Retrieved from https//www.uptodate.com/contents/medications-for-angina-beyond-the-basicsH1Ayerbe, L., Gonzlez, E., Gallo, V., Coleman, C. L., Wragg, A., amp Robson, J. (2016). Clinical assessment of patients with chest pain a systematic review of predictive tools.BMC Cardiovascular Disorders,16(1), 18.Babu, A. S., Noone, M. S., Narayanan, S. M., amp Franklin, B. A. (2012). Exercise based cardiac rehabilitation for unstable angina a case report.Oman medical journal,27(2).
Balla, C., Pavasini, R., amp Ferrari, R. (2018). Treatment of Angina Where Are we.Cardiology,140(1), 52-67.
Bentzon, J. F., Otsuka, F., Virmani, R., amp Falk, E. (2014). Mechanisms of plaque formation and rupture.Circulation Research,114(12), 1852-1866.
Blumenthal, J. A., Feger, B. J., Smith, P. J., Watkins, L. L., Jiang, W., Davidson, J., … amp Kraus, W. E. (2016). Treatment of anxiety in patients with coronary heart disease Rationale and design of the UNderstanding the benefits of exercise and escitalopram in anxious patients WIth coroNary heart Disease (UNWIND) randomized clinical trial.American heart journal,176, 53-62.
Boden, W. E., Franklin, B., Berra, K., Haskell, W. L., Calfas, K. J., Zimmerman, F. H., amp Wenger, N. K. (2014). Exercise as a therapeutic intervention in patients with stable ischemic heart disease an underfilled prescription.The American Journal of Medicine,127(10), 905-911.
Boden, W. E., Padala, S. K., Cabral, K. P., Buschmann, I. R., amp Sidhu, M. S. (2015). Role of short-acting nitroglycerin in the management of ischemic heart disease.Drug Design, Development and Therapy,9, 4793.Coppola, G., Carit, P., Corrado, E., Borrelli, A., Rotolo, A., Guglielmo, M., … amp Novo, S. (2013). ST segment elevations Always a marker of acute myocardial infarction.Indian Heart Journal,65(4), 412-423.
Denn, P., Noonan, B., amp Condon, C. (2017). Typical stable angina in a nurse-led chest pain assessment unit.British Journal of Cardiac Nursing,12(2), 92-97.
Ford, T. J., Corcoran, D., amp Berry, C. (2018). Stable coronary syndromes pathophysiology, diagnostic advances, and therapeutic need. Heart,104(4), 284-292.
Golden State Medical Supply. (2017).Nitroglycerin- nitroglycerintablet. Retrieved fromhttps//dailymed.nlm.nih.gov/dailymed/fda/fdaDrugXsl.cfmsetiddf52ab34-e44c-46f3-8c44-2c1bcb93f28eamptypedisplayInstitute of Quality and efficiency in Healthcare. (2013). Medication for the long term treatment of coronary artery diseases. Retrieved from https//www.ncbi.nlm.nih.gov/books/NBK355311/Iqbal, M. N., Ashraf, A., Muhammad, A., Alam, S., Xiao, S., Ali, S., amp Irfan, M. (2016). Prevalence of Angina Pectoris in relation to various risk factors.PSM Biological Research,1(1), 6-10.
Kim, K. H., amp Schaller, D. J. (2018). Nitroglycerin. Treasure Island (FL)StatPearls Publishing.
Leach, A., amp Fisher, M. (2013). Myocardial ischaemia and cardiac paina mysterious relationship.British Journal of Pain,7(1), 23-30.
MacKenzie, G., Greig, M., Hay, I., amp Pemberton, J. (2017). Competing risk analysis of factors related to long-term incidence of CHD.Journal of Epidemiologyand Community Health,71(1), 33-36.
Massera, D., Graf, L., Barba, S., amp Ostfeld, R. (2016). Angina rapidly improved with a plant-based diet and returned after resuming a Western diet.Journal of geriatric cardiology JGC,13(4), 364.
MedlinePlus. (2019). Living with heart disease and angina. Retrieved from https//medlineplus.gov/ency/patientinstructions/000576.htmMedlinePlus. (2019). Nitroglycerin sublingual. Retrieved from https//medlineplus.gov/druginfo/meds/a601086.htmlODonovan, K. (2013). Nursing assessment of the causes of chest pain.British Journal of Cardiac Nursing,8(10), 483-488.
Physiopedia. (n.d.). Myocardial infarction. Retrieved from https//www.physio-pedia.com/Myocardial_InfarctionRatheesh, A., Sujatha, G., amp Lingappa, A. (2015). Craniofacial pain as manifestation of angina.International Journal of Oral Health Sciences,5(2), 99-99.RxList. (2019). Nitrostat. Retrieved from https//www.rxlist.com/nitrostat-drug.htmdescriptionSaid, S. A., Bloo, R., de Nooijer, R., amp Slootweg, A. (2015). Cardiac and non-cardiac causes of T-wave inversion in the precordial leads in adult subjects A Dutch case series and review of the literature.World Journal of Cardiology,7(2), 86.
van Rooy, M. J., amp Pretorius, E. (2014). Obesity, hypertension and hypercholesterolemia as risk factors for atherosclerosis leading to ischemic events.Current Medicinal Chemistry,21(19), 2121-2129.
Vrints, C. J., Senior, R., Crea, F., amp Sechtem, U. (2016). Assessing suspected angina requiem for coronary computed tomography angiography or exercise electrocardiogram.European Heart Journal,38(23), 1792-1800
Zetta, S., Smith, K., Jones, M., Allcoat, P., amp Sullivan, F. (2011). Evaluating the angina plan in patients admitted to hospital with angina a randomized controlled trial.Cardiovascular Therapeutics,29(2), 112-124.

Looking for a Similar Assignment? Order now and Get 10% Discount! Use Coupon Code "Newclient"