1) Describe how to formulate and test hypothesis about a population mean and/or a population.
A hypothesis essentially refers to the prediction of the expected outcome of a research process. When one intends to research a particular subject, event or outcome, he ought to state his expected outcome. There are two types of hypotheses; null and alternate hypotheses. The null hypothesis refers to what the researcher is trying to nullify, disapprove or reject. In testing the hypothesis, the researcher attempts to prove the hypothesis either wrong or right. In hypothesis testing, the researcher needs to first state both the null and alternate hypotheses. The researcher then needs develops an analysis plan which describes how to use the data to test the hypothesis and determine the appropriate statistical test. The researcher then analyses the data in order to determine the value for the test statistic. Lastly, the researcher interprets the results which involves accepting or rejecting null hypothesis.
The test applies a methodological approach which separates the process from the researcher’s bias. However, the hypothesis testing is still susceptible to errors. Two main types of errors are the type I error also called the alpha error and the type II error also referred to as the beta error. The alpha error refers to the rejection of the null hypothesis when the actual position should be the acceptance of the null hypothesis. The beta error, on the other hand, is the rejection of the hypothesis and acceptance of the null hypothesis while ideally it is the hypothesis that was right.
2) Explain the differences between the regression model, the regression equation, and the estimated-regression equation.
The regression model essentially refers to statistical models that employ regression analysis to illustrate the change in one or more variables when a set of variables change. The regression model, can therefore, be employed in the analysis of variations by changing a set of different variations. It helps in the decision making process as it would bring out the effects of given variable in the model. It should be noted that the model helps in the identification of constant variables or variables that have insignificant effects in models. This information could be utilized in the decision making process by focus on the significant change variables.
The regression equation refers to the typical regression equation that takes the form y = a + bx + c. In this equation, the variables represent the three main components in an equation. These are the dependent variable, which is represented by y. The independent variable is represented by x, c represents the constant in the equation. Using this equation, the regression models that are linear in nature can be manipulated to show the value of the dependent variable with the fluctuations in the independent variables. The estimated regression equation employs the use of a dependent variable that is already estimated to determine the other variables, that is, the independent variable. It take the form of y^ = a + bx.
3) Describe the assumptions necessary to conduct statistical tests involving the hypothesized-regression model.
The hypothesized regression model works on the following assumptions. One, the variable occur in a linear pattern. This assumption usually called linearity assumes that the independent variables occur in a linear pattern and do not deviate substantially away from the residual plot. The variables that fall substantially away from the residual plot are considered non linear. The second assumption is homoskedasticity. This refers to the constant variance of the independent variables from the residual line. The sum of the variances should equal to zero. The assumption works on the premise that the variances are only minimal and that all variables display linearity. This assumption is in consonance to the linearity assumption, in the sense that all the linear deviations should have a common variance. Thirdly and finally, is the assumption of normality. This assumption dictates that the variables occur in a normal distribution along the residual line. As such, all the variables in the populace conform to the pattern of occurrence. The assumption essentially reinforces the earlier two assumptions of linearity and homoskedasticity.
4) Explain how variable selection procedures can be used to choose a set of independent variables for an estimated-regression equation.
In choosing the set of independent variables the researches need to ensure they meet the following requirements. The variables’ place in the equation must not be ambiguous. It needs to be theoretically sound. The variable’s estimated coefficient needs to be testing through the t-test for significance in the expected direction. The overall fit of the equation need to improve even with the adjustment for the degrees of freedom on the addition of the independent variables. Lastly, the other variables in the equation ought not to show significant changes on addition of the variable to the equation. The procedures mentioned above need to be manipulated to identify and chose only the best independent variables. The process involves the use of trial and error methods. The researcher essentially tests a variable applying the mechanics mentioned above for conformity. The process could be done repetitively so as to choose the most suitable independent variables. The selection procedure uses on the variables as they can be subjected to changes unlike the constants.
5) Discuss the different types of forecasting methods.
Forecasting entails the prediction or estimation of the value of a future variable. The forecasting methods range from time series applications, to regression analysis and simulation among other techniques. Time series entails the process of forecasting future variables through the analysis of the historical data already available. The time series uses the trends in the historical data to give an estimate of the future variable. On the other hand, linear regression uses the identification of the independent variables to forecast the future dependent variable. Once the independent variable that would prevail at the time of the event is predicted, the formula is used to forecast the future variable. The regression analysis facilitates forecasting of the future variable even with different values for the independent variable. Simulation entails where the variables are estimated using probabilities and chances of occurrences. Simulation essentially creates a dummy occurrence of the event and shows the likely outcome in the event of set of actions prevailing. The simulated conditions are then presented in appreciation of their probability of occurrence. This helps in forecasting likely results and variables in the future.
6) Economic crises in one country often have an impact on the economic or business measures of other countries.
For example, economic and monetary crises in Asia in 1997, the Argentine debt crisis of 2001, and more recently the European currency crisis of 2011, have impacted businesses, currency markets, and future financial forecasts. For this question, do some research on one of these economic events, and relate how an economic crisis in one country can impact the wider global economy. Also, indicate what impact the crisis would have on a forecaster's ability to analyze and forecast future trends.
The debt crisis in Greece refers to the enormous deficits that Greece nation faces. It has affected the Greek economy compelling the government and other employers to introduce wage cuts. Demand for products is also low. The crisis has escalated into the larger Europe and threatens to lead to the collapse of the Euro. This could lead to a ripple of effects which would affect the entire global economy. The consequences include the inability to sell products to the European market which constitutes a huge market for the consumption of world industrial products. In addition, the collapse of the Euro would mean the European nations would be unable to service their loans and financial obligations. The consequence would be the collapse of the world financial systems as the banks would be highly indebted. In addition, the collapse of the Euro would render the Euros useless or of little utility given the likely inflationary effects on the currency.
Finally, the debt crisis threatens to trigger a recession in the globe due to the deficits that would be posted by businesses in the Euro zone. Recession would reduce the economic development and prosperity of the global nations. The crisis reduces the ability of forecasters to forecast the trends of the future. This is because the crises are not predictable and the gravity of the crises depends on the actions pursued by a number of market determinants.
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