Exploring Two–Variable Data

A visible pattern among residuals indicates an exceptionally high correlation between variables modeled linearly.

The absence of randomness in residuals implies that this model fits perfectly for prediction purposes.

Patterns within residuals mean that individual predictions will all be equally accurate or inaccurate across datasets modeled.

The presence of patterns suggests that there is non-linearity not captured by the linear model applied to these data.

By identifying outliers

By calculating the correlation coefficient

By analyzing the trend from left to right

By comparing the clusters

Outliers will always decrease confidence intervals making them more precise but potentially misleading.

Outliers could significantly increase or decrease the calculated correlation coefficient, leading to possible Type I or II errors.

Presence of outliers will ensure that any hypothesis test performed will meet necessary conditions without transformation.

Outliers uniformly distribute across datasets and thus generally have no effect on hypothesis tests concerning correlation.

It decreases

The effect is unpredictable

There's no change

It increases as well

Dependent variable

Correlation variable

Response variable

Explanatory variable

Correlation coefficient

Regression coefficient

p-value

Hypothesis test result

A data point that is significantly different from the rest of the data

A data point that has a significant impact on the regression line or fitted model

A data point that breaks the overall trend

A data point with high leverage

The width of the confidence interval will decrease.

The change in variability does not affect confidence intervals.

The width of the confidence interval will remain unchanged.

The width of the confidence interval will increase.

Misinterpreting the code used to calculate, giving incorrect results.

Not collecting data properly, leading to skewed distributions and higher results.

Lack strong evidence supporting the alternative hypothesis thought prior to conducting the study.

Confusing terms like standard deviation and variance, which caused errors in computation.

Sampling error is likely the cause of the discrepancies observed in standard deviation, rather than true population variability.

Standard deviations are unaffected by sampling methods, thus reflecting the exact variability within the populations being compared.

Means are unreliable indicators of variation, so the difference in standard deviations is irrelevant.

While both schools might have similar average height, students vary more in their heights at one school than the other.