Statistical Inference: Z-Distribution, T-Distribution, and Regression
Chapter 6: Standard Error (SE)
The standard error (SE) is the standard deviation of the sampling distribution of a statistic. It measures the precision of the sample statistic as an estimate of the population parameter. A z-distribution is the standard normal distribution with a mean of 0 and a standard deviation of 1. It is used for testing hypotheses about a single population mean or proportions when σ is known. The T-distribution is a family of distributions that are similar to the normal distribution
Read MoreVehicle Tax Analysis: Price, Age, and Regression Insights
1. Interpreting the Slope in the Simple Linear Regression Model
A 1% increase in price is associated with a 0.8% increase in taxes. Given that the increase is less than 1%, the vehicle tax is regressive, not progressive, meaning that more expensive cars pay proportionally less tax.
rate = exp(b1) * exp(0.8161 * log_price) = exp(b1) * (exp(log_price))^0.8161 = exp(b1) * (price)^0.8161
Hence, an increase in the price of 1% implies an increase in the rate of (1.01)^0.8161 = 1.00815, that is, an increase
Read MoreMastering Math: Exponents, Roots, Polynomials, and More
Powers
Power = (Base)exponent
Properties of Powers
- 1st
- 2nd
- 3rd
- 4th
- 5th
- 6th
- 7th
- 8th
- 9th
Scientific Notation
A) Mt indicates the number of zeros to the right.
B) Mor indicates tenths. No. If I have a high ten, and M is positive, add zeros to the number as indicated by the M.
Roots
A) Numeric values of a radical. If the radical is a positive number, the solution is a unique positive root.
B) If the radical is negative and the index is even, the solution is a negative root.
C) Based on a positive, even index, there is
Read MoreHypothesis Theory: Types, Characteristics, and Formulation
Hypothesis Theory
A hypothesis is an assumption that establishes a relationship between two or more variables, expressed as facts, events, or factors. It must be tested to be accepted as valid.
Role of a Hypothesis
- Guides and directs an investigation.
- Assumptions should be deduced from the problem and aims of the study.
- Must be consistent with the theoretical framework.
- Determines the type of study and design methodology.
Characteristics of a Hypothesis
- Must refer to a real situation with a defined context.
Key Concepts in Statistics: Data Analysis and Metrics
Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data.
Population vs. Sample
- Population: All items of interest (e.g., all cars bought in Ontario last year). Note: It is often impossible to collect all these data points.
- Sample: Items randomly selected from the population (e.g., 1000 cars bought in Ontario last year).
Parameter vs. Statistic
- Parameter: A numerical description of the population.
- Statistic: A numerical description
Biostatistics in Medicine and Public Health: Key Concepts
Biostatistics in Medicine and Public Health
Biostatistics is the science that helps us make sense of data. It can be as simple as summarizing a distribution or identifying whether two variables are correlated. Statistics is crucial for biomedical science as it enables us to make sense of data that have been collected in an experiment or survey and to assess whether the observed result may just have arisen by chance.
- It tells us how to collect, organize, analyze, and interpret the collected numerical