Introduction to Correlation and Regression Analysis
How many items (data points) will you display for each variable? Scatter plot charts are good for relationships and distributions, but pie charts should . Good for showing the relationship between two different variables where one A good example of a bubble chart would be a graph showing marketing. Keywords: Data presentation, Data visualization, Graph, Statistics, Table effective methods of presenting data, which are the end products of research, If one wishes to compare or introduce two values at a certain time point, . y-axes and are used to investigate an association between two variables. An equation is a mathematical way of looking at the relationship between concepts or items. A variable represents a concept or an item whose magnitude can be represented by a This does not mean that y is the product of two separate quantities, f and x but rather We may look at functions algebraically or graphically.
All Modules Introduction to Correlation and Regression Analysis In this section we will first discuss correlation analysis, which is used to quantify the association between two continuous variables e. Regression analysis is a related technique to assess the relationship between an outcome variable and one or more risk factors or confounding variables. The outcome variable is also called the response or dependent variable and the risk factors and confounders are called the predictors, or explanatory or independent variables.
In regression analysis, the dependent variable is denoted "y" and the independent variables are denoted by "x". The term "predictor" can be misleading if it is interpreted as the ability to predict even beyond the limits of the data. Also, the term "explanatory variable" might give an impression of a causal effect in a situation in which inferences should be limited to identifying associations. The terms "independent" and "dependent" variable are less subject to these interpretations as they do not strongly imply cause and effect.
Correlation Analysis In correlation analysis, we estimate a sample correlation coefficient, more specifically the Pearson Product Moment correlation coefficient.
The correlation between two variables can be positive i. The sign of the correlation coefficient indicates the direction of the association. The magnitude of the correlation coefficient indicates the strength of the association.
- Introduction to Correlation and Regression Analysis
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A correlation close to zero suggests no linear association between two continuous variables. You say that the correlation coefficient is a measure of the "strength of association", but if you think about it, isn't the slope a better measure of association? We use risk ratios and odds ratios to quantify the strength of association, i.
The analogous quantity in correlation is the slope, i. And "r" or perhaps better R-squared is a measure of how much of the variability in the dependent variable can be accounted for by differences in the independent variable. The analogous measure for a dichotomous variable and a dichotomous outcome would be the attributable proportion, i. Therefore, it is always important to evaluate the data carefully before computing a correlation coefficient.
Graphical displays are particularly useful to explore associations between variables. The figure below shows four hypothetical scenarios in which one continuous variable is plotted along the X-axis and the other along the Y-axis. Scenario 3 might depict the lack of association r approximately 0 between the extent of media exposure in adolescence and age at which adolescents initiate sexual activity.
Example - Correlation of Gestational Age and Birth Weight A small study is conducted involving 17 infants to investigate the association between gestational age at birth, measured in weeks, and birth weight, measured in grams. We wish to estimate the association between gestational age and infant birth weight. In this example, birth weight is the dependent variable and gestational age is the independent variable.
The data are displayed in a scatter diagram in the figure below. Stacked bars are not good for comparison or relationship analysis. The only common baseline is along the left axis of the chart, so you can only reliably compare values in the first series and for the sum of all series. We used to draw those on blackboards in school. Line charts are among the most frequently used chart types. Use lines when you have a continuous data set. These are best suited for trend-based visualizations of data over a period of time, when the number of data points is very high more than With line charts, the emphasis is on the continuation or the flow of the values a trendbut there is still some support for single value comparisons, using data markers only with less than 20 data points.
A line chart is also a good alternative to column charts when the chart is small. Timeline Charts The timeline chart is a variation of line charts. Obviously, any line chart that shows values over a period of time is a timeline chart.
The only difference is in functionality — most timeline charts will let you zoom in and out and compress or stretch the time axis to see more details or overall trends. The most common examples of a time-line chart might be: For line charts, the axis may not start from zero if the intended message of the chart is the rate of change or overall trend, not exact values or comparison. In line charts, time should always run from left to right.
Do not skip values for consistent data intervals presenting trend information, for example, certain days with zero values. Remove guidelines to emphasize the trend, rate of change, and to reduce distraction. Use a proper aspect ratio to show important information and avoid dramatic slope effects.
For the best perception, aim for a degree slope. Area charts will fill up the area below the line, so the best use for this type of chart is for presenting accumulative value changes over time, like item stock, number of employees, or a savings account.
Do not use area charts to present fluctuating values, like the stock market or prices changes. Stacked Area Stacked area charts are best used to show changes in composition over time. A good example would be the changes of market share among top players or revenue shares by product line over a period of time. Stacked area charts might be colorful and fun, but you should use them with caution, because they can quickly become a mess.
Not in data visualization, though. These charts are among the most frequently used and also misused charts. The one on the right is a good example of a terrible, useless pie chart - too many components, very similar values. A pie chart typically represents numbers in percentages, used to visualize a part to whole relationship or a composition.
Pie charts are not meant to compare individual sections to each other or to represent exact values you should use a bar chart for that.
What is a Scatter Plot and When to Use It
When possible, avoid pie charts and donuts. I mean, like, never! You might think that you could use a stacked donut to present composition, while allowing some comparison with an emphasis on compositionbut it would perform badly for both. Use stacked column charts instead.
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Make sure that the total sum of all segments equals percent. Ideally, there should be only two categories, like men and women visiting your website, or only one category, like a market share of your company, compared to the whole market. Scatter Charts Scatter charts are primarily used for correlation and distribution analysis. Scatter charts can also show the data distribution or clustering trends and help you spot anomalies or outliers.
A good example of scatter charts would be a chart showing marketing spending vs. Bubble Charts A bubble chart is a great option if you need to add another dimension to a scatter plot chart.
Scatter plots compare two values, but you can add bubble size as the third variable and thus enable comparison. If the bubbles are very similar in size, use labels.
A good example of a bubble chart would be a graph showing marketing expenditures vs. A standard scatter plot might show a positive correlation for marketing costs and revenue obviouslywhen a bubble chart could reveal that an increase in marketing costs is chewing on profits.
Use Scatter and Bubble charts to: Present patterns in large sets of data, linear or non-linear trends, correlations, clusters, or outliers. Compare large number of data points without regard to time. The more data you include in a scatter chart, the better comparisons you can make. Present relationships, but not exact values for comparisons. Map Charts Map charts are good for giving your numbers a geographical context to quickly spot best and worst performing areas, trends, and outliers.
If you have any kind of location data like coordinates, country names, state names or abbreviations, or addresses, you can plot related data on a map. A good example would be website visitors by country, state, or city, or product sales by state, region or city. When to use map charts? If you want to display quantitative information on a map.
To present spatial relationships and patterns. When a regional context for your data is important. To get an overview of the distribution across geographic locations. Only if your data is standardized that is, it has the same data format and scale for the whole set.
Gantt Charts Gantt charts were adapted by Karol Adamiecki in But the name comes from Henry Gantt who independently adapted this bar chart type much later, in the s. Gantt charts are essentially project maps, illustrating what needs to be done, in what order, and by what deadline.
You can visualize the total time a project should take, the resources involved, as well as the order and dependencies of tasks. But project planning is not the only application for a Gantt chart. It can also be used in rental businesses, displaying a list of items for rent cars, rooms, apartments and their rental periods. To display a Gantt chart, you would typically need, at least, a start date and an end date. Gauges are a great choice to: Show progress toward a goal.
Represent a percentile measure, like a KPI. Show an exact value and meaning of a single measure. Display a single bit of information that can be quickly scanned and understood. The bad side of gauge charts is that they take up a lot of space and typically only show a single point of data. If there are many gauge charts compared against a single performance scale, a column chart with threshold indicators would be a more effective and compact option.
Multi Axes Charts There are times when a simple chart just cannot tell the whole story. If you want to show relationships and compare variables on vastly different scales, the best option might be to have multiple axes. But it comes at a cost. That is, the charts are much more difficult to read and understand. Multi-axes charts might be good for presenting common trends, correlations or the lack thereof and the relationships between several data sets. But multi-axes charts are not good for exact comparisons because of different scales and you should not use this type if you need to show exact values.
Use multi-axes charts if you want to: Display a line chart and a column chart with the same X-axis. Compare multiple measures with different value ranges.