Collecting Data

Each individual divides into predefined categories

Involves several steps

A single-stage process

Entire groups (clusters) are chosen at once instead of individuals

Individuals interested in technology advancements naturally gravitate towards owning electric vehicles, resulting in greater income opportunities.

People earning above-average incomes feel financial pressure and demonstrate wealth through purchasing expensive items like electric cars.

Lurking variables such as education level and environmental consciousness may correlate both with choosing electric vehicles and earning higher incomes.

Electric car ownership boosts social status, therefore indirectly increases chances of professional advancement and career growth.

Response bias

Nonresponse bias

Undercoverage bias

Voluntary response bias

Only individuals meeting certain criteria are chosen.

Every individual has an equal chance of being selected.

Samples are taken at regular intervals from the population.

Individuals are chosen based on convenience.

Mean absolute deviation

Interquartile range (IQR)

Standard error

Mode

The simpler model requires fewer parameters yet predicts training data with slightly better accuracy than complex models.

The complex and simpler models yield more accurate predictions as more variables are introduced into each respective analysis framework.

Both models achieve identical levels of accuracy when applied to large-scale validation datasets after training completion.

The complex model exhibits high accuracy on training data but significantly less accuracy on validation or testing data sets compared to simple models.

Scatterplot with added calculation of Pearson's correlation coefficient ($r$) along with identification of potential outliers or influential points.

Calculation of Spearman's rank correlation coefficient without visual inspection or consideration of possible outliers or influential points.

Creation of side-by-side boxplots comparing SAT scores against discrete ranges or quartiles defined by college GPA levels.

Computing a regression line exclusively based on median values rather than individual data points across SAT scores and GPAs.

The residuals should be approximately normally distributed for each value of the independent variable.

There must be linearity between the independent and dependent variables.

The sum of residuals must equal zero.

The variance of residual terms should be constant across all levels of the independent variable.

Application of blinded designs where subjects don't know if they're receiving treatment or placebo

Implementation of control groups used explicitly designed compare different conditions within study context effectively

Use of technology like computer algorithms that randomly assign treatment groups among study participants

Presence of confounding variables linked both with treatment exposure and outcome measures being studied

Every point in the dataset lies exactly on the regression line.

There is no correlation between the independent and dependent variables.

The variance of the error terms is consistent across all levels of the independent variable.

The linear model may not be appropriate for the data.