# Graphical display of the relationship between two quantitative variables

how you would decide which graphical display and numerical measures to use. with two quantitative variables, then a scatterplot will be used. side-by-side plots(relationship between categorical explanatory and quantative response), two. A graphical display of the relationship between two quantitative variables is a. a pie chart b. a histogram c. a crosstabulation d. a scatter diagram ANS: D PTS: 1. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Graphical display of the relationship between two quantitative variables.

The individual values can be read from the plot and an idea of the relationship between the variables across individuals is obtained. Even if the plot is not used in the final presentation, it may highlight outliers and will help to indicate the appropriate form of analysis to use. For example, the plot below comes from a study from the BMJ, looking at the association between age and ear length.

They found a weak positive association, meaning higher values of 'age' are associated with higher values of 'ear length' the article was published in the Christmas edition, where more light-hearted articles are encouraged.

- Comparing Two Quantitative Variables

Why do old men have big ears? Alternatively, the same variable may be measured in a matched pair of individuals. Any 'pairing' that is inherent because of the way in which the data was collected should be retained in both displaying and analysing the data. Line diagrams are often used whereas a scatterplot is generally more appropriate. Milliner et al, Results of long-term treatment with orthophosphate and pyridoxine in patients with primary hyperoxaluria, New England Journal of Medicine,;Vol ,No.

Measurements were made of calcium oxalate inhibition in 12 patients, pre and post treatment. The authors displayed the data as a line-plot.

### Comparing Two Quantitative Variables | STAT

The values for each patient are shown pre and post treatment and are joined by lines to show the within person pairing of the measurements. Inhibition of the formation of calcium oxalate crystals during treatment with orthophosphate and pyridoxine in 12 patients with primary hyperoxaluria. The line plot shows that all individuals have values that rise during treatment. One individual shows a very large increase from about 25 pre-treatment to about during treatment as illustrated by the steeply rising diagonal line.

The same data is presented below as a scatterplot: The line of equality no change in values pre to during treatment is shown as a dashed line on the display. All points lie above the line of equality showing that values rose for each individual.

## Graphical Displays: Two Variables

Whilst the same information is given by the two displays, the scatterplot uses only one point to represent each individual compared to 2 points and a line for the line diagram. The line diagram may be confusing to assess if there are changes in various directions, the scatterplot with the line of equality superimposed if necessary is easier to interpret.

No information is lost, the display clearly shows the relationship between the variables and also highlights possible outliers. We saw an example earlier of the times it takes for a scorpion to capture its prey presented as a dot plot.

Optimal sting use in the feeding behavior of the scorpion Hadrurus spadix. Dot plots can also be used to look at the differences between the distributions of groups. In the example below, E coli specific SigA values are typically lower and also less spread out in the 'White UK' category. Dot plots can be used to look at whether values in one group are typically different from values in another group.

In the example above, the plot shows it typically takes slightly longer for a scorpion to catch a prey with low activity than high activity. Archives of Disease in Childhood,;71,F Horizontal bars denote medians for each group.

The table below shows how social class varied between the two areas of the baby check scoring system. In both areas the mothers were mostly from social class III manual.

This table shows how illness severity was related to baby-check score. We can see the association of increasing severity with increasing score.

The initial impression was not recorded for two babies. For example, if we substitute the first Quiz Average of Using this value, we can compute the first residual under RESI by taking the difference between the observed y and this fitted: Similar calculations are continued to produce the remaining fitted values and residuals.

What does the slope of 0. The slope tells us how y changes as x changes.

That is, for this example, as x, Quiz Average, increases by one percentage point we would expect, on average, that the Final percentage would increase by 0. Coefficient of Determination, R2 The values of the response variable vary in regression problems think of how not all people of the same height have the same weightin which we try to predict the value of y from the explanatory variable x.

The amount of variation in the response variable that can be explained i.

Since this value is in the output and is related to the correlation we mention R2 now; we will take a further look at this statistic in a future lesson. Residuals or Prediction Error As with most predictions about anything you expect there to be some error, that is you expect the prediction to not be exactly correct e.

Also, in regression, usually not every X variable has the same Y variable as we mentioned earlier regarding that not every person with the same height x-variable would have the same weight y-variable.

These errors in regression predictions are called prediction error or residuals.