Exploring Two–Variable Data

The sum of squared residuals

The range of residuals

The product of squared residuals and regression coefficients

The sum of absolute deviations from the mean

Pearson's correlation coefficient (r)

P-value from an ANOVA test

Exponential growth rate

Chi-square statistic

The increase in temperature is a confounding variable that affects both ice cream sales and drowning incidents.

There is no plausible explanation; the correlation must be coincidental and not indicative of any relationship.

Ice cream sales cause an increase in drowning incidents due to people swimming shortly after eating.

Drowning incidents lead to an increase in ice cream sales as a coping mechanism for stress.

To confirm if there's a linear relationship justifying regression analysis.

To calculate the correlation coefficient visually without statistical software.

To determine if any transformations are needed to achieve normality.

To identify any possible causation between variables depicted in data points.

Mode-mode line.

Average deviation line.

Least squares regression line.

Median-median line.

Coefficient of determination ($r^2$).

Pearson's correlation coefficient ($r$).

Standard deviation of x-values ($s_x$).

Mean absolute deviation (MAD).

Despite being identified as high-leverage observations according solely upon their predictor variable value magnitudes might not necessarily affect fitted model robustness unless accompanied associated large residuals too.

They disproportionately influence slope and intercept estimates thus potentially distorting corresponding confidence intervals' width and location.

Discovering higher Cook's distances suggests reconsideration regarding those points' inclusion due primarily because they exert undue influence over overall model parameters.

High-leverage points generally necessitate additional investigation since presence alone does indicate significant alteration expected outcome distributions even without notable contribution toward total sum square errors (SSE).

-0.8

0.4

0.64

-0.64

No, as long as their correlation coefficients are equal.

Yes, but only if one dataset contains more points than another does.

Yes, if they have different spread or outliers but similar overall trends.

No, because identical lines mean they must have identical plots.

Data distributed evenly along a clear linear trend without significant outliers.

A large dataset where outliers have minimal impact on slope determination.

A small dataset where each individual point heavily influences slope calculation.

Multiple datasets yielding similar slopes when performing separate regressions analyses.