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Why do so many of life's events share the same characteristics as the central limit theorem? Why are estimations and confidence intervals important? When might systematic sampling be biased? Explain. What roles do confidence intervals and estimation play in the selection of sample size?

The response addresses the queries posted in 700 words with four references.

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The response addresses the queries posted in 700 words with references.

// As per the directions, we will write about the characteristics of central limit theorem that are shared in events of life. Then, we will write about the importance of estimations and confidence intervals.//

The Central Limit Theorem in concern to the non-mathematical definition can be stated that the aggregate or the mean of the large random variables or events is directed towards the formation of a bell-curve as it is there in normal distribution. For instance: If the case of rolling of a dice is taken, the distribution of the mean or the average of the numbers on the dice will be normally distributed. Each rolled number or events can be normally distributed. This is due to the reason that each event or rolled number is approximately equal or close to the mean or the average. It can be said that the lesser the event closer to the average or the mean, it has fewer chances of being normally distributed (Adams, 2009).

The large number of events in life occurs randomly. It is due to the multiple and differentiating factors with ...

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The response addresses the queries posted in 700 words with references.

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Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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