## Elementary Statistics Theory Assignment Help

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### Regression Analysis

Regression analysis is one of the data analysis methods used in statistics. It involves the estimation of relationships between dependent and independent variables. Regression analysis assesses the relationship between these two variables. Also, it can model the future relationship between dependent and independent variables.

A linear relationship between the intercept and slope must exist between the dependent and independent variables

- The independent variable should not be random
- The error (residual) value should be zero
- The error (residual) value should be constant across all observations
- The value of the error (residual) should not be correlated across all observations
- Lastly, the values of the residual (error) should follow a normal distribution

### Simple linear regression

The equation below expresses a simple linear model:

Y = a + bx + ϵ

In the equation:

- Y represents the dependent variable
- X is the explanatory or independent variable
- a is the intercept
- b represents the slope
- ϵ is the residual (error)

### Multiple linear regression analysis

Multiple linear regression analysis allows multiple independent variables. The model can be mathematically represented as below:

Y = a + bX1 + cX2 + dX3 + ϵ

In the equation:

- Y is the dependent variable
**X1, X2, and X3 represent the explanatory (independent) variables****a is the intercept****b, c and d are the slopes**- ϵ is the residual (error)

The same conditions in a simple linear model are followed in multiple linear regression. However, there is another mandatory condition since there are several independent variables:

**Non-collinearity condition**– This condition states that the independent variables must show a minimum of correlation with each other. A high correlation means it will be difficult to assess the true relationship between independent and dependent variables

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### Poisson Distribution

Poisson distribution is a statistical distribution function that was developed by French mathematician Simeon-Denis Poisson. It is used to characterize events with very low chances of happening within some definite space or time. Poisson distribution is used by businessmen to forecast sales and the number of customers in particular seasons of the year.

For example, suppose every Saturday night, a textbook store rents out an average of 300 books. With this information, we can predict the probability that more books will sell on the coming Saturday nights.

#### How to calculate the Poisson distribution

The formula for calculating the Poisson distribution is:

P(x; μ) = (e-μ * μx) / x!

Where:

- ! – factorial
- μ (can also be written as λ)– is the expected number of occurrences. It is sometimes called the rate parameter or event rate

**Solved Example**

**Question 1:**The city of New York has an average number of major storms of 2 per year. Find the probability that the city will be hit by 3 storms next year.

Our statistics homework helpers have used a step by step approach to help you understand the solution.

**Solution**

**First step:**

Determine the components that should be put in the equation:

- μ = The average number of storms per year, historically is 2
- x = The number of storms that might hit next year is 3
- e = is a constant number, known as Euler’s number. It is always represented by 2.71828

**Second step**

Use the Poisson distribution formula. Insert the values:

P(x; μ) = (e-μ) (μx) / x!

= (2.71828 – 2) (23) / 3!

= 0.180

From our calculation, the probability of 3 major storms hitting New York next year is 0.180 or 18%. An IBM SPSS software can be used to calculate Poisson distribution for real-life situations. Performing the calculations manually can take a considerable amount of time, especially if the data set is not simple.

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### Central Limit Theorem

This theory states that as the sample size gets larger, the sampling distribution of the sample means approaches a normal distribution. The fact holds regardless of the shape of the population distribution. Also, the theory is true for sample sizes that are over 30. To explain the central limit theorem better, we can say that when we take more large samples, our sample means the graph will look more like a normal distribution.

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Other topics under elementary statistics theory covered by our experts are:

- Stochastic Modeling and Bayesian Inference
- Sample Surveys
- Poisson
- The moment generating function
- Point estimation: Method of Moments Estimation
- Combinatorial methods
- Descriptive statistics including some exploratory data analysis
- Concepts of statistical inference
- Expectation and variance
- Regression and ANOVA with Minitab
- Inference for correlation coefficients and variances
- Hypothesis testing and prediction
- Quantitative Methods
- Conditional probability
- Maximum likelihood estimation
- Bayes’ theorem
- Linear regression analysis
- Applied Business Research and Statistics
- Contingency tables
- Model estimation
- Sampling distributions of statistics
- Probability: Axiomatic Probability
- Uniform and normal distributions.
- Interval estimation
- Sampling Theory
- elementary statistics
- Random variables: discrete and continuous random variables
- Testing statistical hypotheses: One-sample tests and Two-sample tests
- Important distributions of statistics
- Rank-based nonparametric tests and goodness-of-fit tests
- Joint and conditional distributions

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