Exploring Two–Variable Data

Pearson's correlation coefficient (r)

P-value from an ANOVA test

Exponential growth rate

Chi-square statistic

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

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.

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).

A line that minimizes the sum of squared residuals.

A line that passes through (0, 1).

A line that fits the data points exactly without any residuals.

The line that connects the first and last data points in a scatterplot.

-0.8

0.4

0.64

-0.64

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.

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.

Cannot be determined without further information.

Less than 0.

Between 0 and 1.

Exactly 1.