Slopes

Simple random sampling

Convenience sampling

Stratified random sampling

Systematic sampling

It proves that changes in one variable will cause changes in another since they are statistically related.

It shows that any value within its range will have no effect on determining causality within data trends.

It only quantifies how well future samples could estimate this slope, but cannot establish cause-and-effect relationships.

It reflects all possible values of correlation coefficients establishing a direct causal connection.

Population mean

Sample mean

Standard deviation of the sample

Residuals

The sample size should be at least 30 for normal distribution

The sample regression line accurately represents the population regression line

The standard deviation of the residuals should be known

The population standard deviation should be small

The sample median.

The population mean ($\mu$).

The population slope ($\beta$).

The sample mean ($\bar{x}$).

Residuals are normally distributed.

Residuals have constant variance across all levels of x.

Residuals equal zero for all observations.

Each residual is larger than the previous residual.

The difference between the sample mean and the population mean

A range of values that is likely to contain the true population parameter (with a level of confidence)

The exact value of the population parameter

The range of values that is likely to contain the sample mean

Judgmental (or purposive) sampling

Multistage Sampling

Cluster Sampling

Simple random sampling

There is evidence to suggest that there is a statistically significant linear relationship between the two variables.

The correlation coefficient between the two variables must be zero.

There is definite causal relationship between the independent and dependent variables.

The slope of the regression line can accurately predict values outside of the observed data range.

To predict future outcomes based on past data without considering variability.

To determine if there is no relationship between the independent and dependent variable.

To estimate the true slope of the population regression line within a certain level of confidence.

To calculate the exact value of the correlation coefficient between two variables.