Slopes

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

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.

Mean of the sample

Standard deviation of the population

Sample size, level of confidence, and degree of variation in the sample

Margin of error and point estimate

There is evidence of a statistically significant linear relationship.

There is no evidence of any relationship between the variables.

The slope of the regression line must be positive.

The variability in y cannot be explained by x at all.

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 in intervals suggests a lack of consistency in variance between datasets.

The model lacks robustness since the intervals do not exactly match.

Inference on robustness cannot be made without knowing the confidence level.

The model is likely robust as the intervals are similar across datasets.

Predictions made outside the observed data range assume existing linear relations continue unchanged, potentially overlooking other influences.

Extrapolations always produce accurate forecasts because high R-squared values validate extended linearity regardless of where.

Predictions confirm underlying causes since mathematical models represent reality fully ensuring accuracy even far from known points.

Since r-values measure strength direction trend, therefore stretching them beyond provided information maintains their integrity completely unaffected by distance.

Standard error of the estimate

Variability of the sample mean

Dispersion of the sample values around the population mean

Dispersion of the residuals around the mean