Exploring Two–Variable Data

By identifying outliers

By calculating the correlation coefficient

By analyzing the trend from left to right

By comparing the clusters

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.

$r > .5$

$r = -1$

$r = 0$

$r < -.5$

Performing a Pearson correlation coefficient analysis between X and Y.

Conducting a regression with both $X$ and $X^2$ as predictor variables.

Applying a t-test comparing high scorers' and low scorers' average time on homework.

Utilizing a one-way ANOVA with different time categories of homework.

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.

Variance in the explanatory variable does not affect the model's predictive accuracy on new data.

The new dataset will automatically conform to the original model's predictions.

The model may not fit well if the relationship between variables differs.

The predictive accuracy will remain consistently high due to the high R-squared value.

The general shape of the plotted points

The presence of outliers

The overall strength of the data

The direction of the scatter