Essential Statistical Concepts and Tests
Simple Linear Regression
Purpose: Predict a numerical outcome (dependent variable Y) from a numerical predictor (independent variable X).
Equation: Y = a + bX
a (intercept): Predicted Y when X = 0
b (slope): For each 1-unit increase in X, Y increases/decreases by b units.
Example: Income = 20000 + 3000 × YearsOfEducation → Each extra year of education predicts $3,000 more income.
R² (Coefficient of Determination): Tells us how much of the variation in Y is explained by X. Ranges from 0 to 1.
Interpretation:
Understanding Statistics: Key Concepts and Applications
Understanding Statistics
Statistics is a branch of mathematics and science that deals with collecting, organizing, analyzing, interpreting, and presenting data to make informed decisions. It plays a crucial role in almost every field, from business and economics to healthcare and social sciences, enabling individuals and organizations to draw meaningful conclusions and forecast future trends.
Definition of Statistics
As a Singular Noun:
Statistics refers to the science of collecting, analyzing, and
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Linear Regression: Test Scores vs. Hours Studied
Consider the following linear regression equation: Test Scores = 45 + 5(Hours Studied)
- The Test Scores variable is the outcome variable. It is what the model is trying to predict.
- Hours Studied is the explanatory variable. It is used to explain or predict changes in the test scores.
- The slope coefficient associated with Hours Studied is 5. This indicates that for every additional hour spent studying, the model predicts an increase of 5 points in the test
Statistics Essentials: Stem Plots, Quartiles, Correlation
Stem Plots
To make a stem plot:
- Separate each observation into a stem (all but the final digit) and a leaf (the final digit). Stems may have as many digits as needed, but each leaf contains only a single digit.
- Write the stems in a vertical column with the smallest at the top, and draw a vertical line to the right of this column. Include all stems needed to span the data, even with no leaves.
- Write each leaf in the row to the right of its stem, in increasing order out from the stem.
Quartiles and Interquartile
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Correlation vs. Causation in Research
Karpinski found, in a correlation study, that students who used Facebook had lower GPAs than those who didn’t (3.0 to 3.5 vs. 3.5 to 4.0) and spent less time studying (1-5 hours vs. 11-15 hours). However, correlation doesn’t equal causation. People who prefer more leisure time are more likely to be drawn to distractions like Facebook. Alternatively, students who use Facebook might also spend more time on other non-studying activities, such as sports or music.
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