If a data set contains n paired values on two variables x(independent) and y(dependent), then their plot is called:
Scatter diagram
Understanding Plots for Paired Data
When we collect data, we often have observations on two or more characteristics for each item or individual. If we have measurements for two variables, say x and y, for n different subjects or instances, this forms a data set of n paired values. The question specifies that x is the independent variable and y is the dependent variable.
What are Independent and Dependent Variables?
In many analyses, we look at how one variable might influence or be related to another.
- The independent variable (x) is the one that is thought to influence or cause a change in the dependent variable. It is often plotted on the horizontal axis (x-axis).
- The dependent variable (y) is the one that is being measured or observed and is expected to change in response to the independent variable. It is usually plotted on the vertical axis (y-axis).
We want a visual way to see how these paired values relate to each other.
Analyzing Plot Options for Paired Data
Let's consider the given options and their uses:
- Dendogram: This is a diagram used in hierarchical clustering to show the arrangement of clusters produced by clustering algorithms. It represents similarity or distance between data points or clusters and is not used for plotting individual paired (x, y) values to show their direct relationship.
- Point diagram: While any plot consists of points, "point diagram" is not a standard, specific term used in statistics to describe the graph for paired (x, y) data.
- Scatter diagram: A scatter diagram, or scatter plot, is specifically designed to display the relationship between two quantitative variables. For each pair of observations \((x_i, y_i)\), a single point is plotted on a two-dimensional grid. The position of the point is determined by its x-value and y-value. This type of plot is ideal for visualizing patterns, trends, and potential correlations between an independent and a dependent variable.
- Correlogram: This type of graph is typically used to display correlation coefficients. For example, in time series analysis, an autocorrelation function (ACF) plot (a type of correlogram) shows the correlation of a variable with itself at different time lags. A correlogram can also display a matrix of correlations between multiple variables. It does not plot the individual paired data points directly.
Identifying the Correct Plot
Given a data set of n paired values \((x_i, y_i)\) where x is independent and y is dependent, the standard and most appropriate graphical tool to visualize the relationship between these two variables is the Scatter diagram. Each point on the scatter diagram represents one pair of values from the data set.
| Plot Type | Common Use | Suitable for Paired (x, y) Data (Independent vs. Dependent)? |
|---|---|---|
| Dendogram | Hierarchical Clustering | No |
| Point diagram | General term, not specific statistical plot | Not standard |
| Scatter diagram | Relationship between two quantitative variables | Yes, standard method |
| Correlogram | Displaying correlations (e.g., autocorrelation, correlation matrix) | No |
Therefore, a data set containing n paired values on two variables x (independent) and y (dependent) is plotted using a Scatter diagram.
Revision Table: Common Statistical Plots
| Plot Name | What it Shows |
|---|---|
| Scatter Diagram | Relationship between two quantitative variables |
| Histogram | Frequency distribution of a single variable |
| Bar Chart | Comparison of values across categories |
| Line Chart | Trends over a continuous range (like time) |
| Box Plot | Distribution summary (median, quartiles, spread, outliers) for one or more groups |
Additional Information on Scatter Diagrams
Scatter diagrams are powerful tools in the initial stages of data analysis. They help analysts quickly understand if a relationship exists between two variables, what shape the relationship takes (linear, curved), how strong it is, and if there are any unusual observations (outliers). The pattern of points on a scatter diagram can suggest whether a correlation exists and provide insights before applying more complex statistical models like linear regression.
Similar Questions
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Important Questions from Correlation Analysis
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): If the securities with less than perfect negative correlation between their price movements are combined, portfolio risk can be reduced significantly.
Reason (R): The term with negative correlation has the effect of reducing the computed value of total portfolio risk, given other terms that are positive.
In the light of the above statements, choose the most appropriate answer from the options given below:
X, Y and Z are three uncorrelated variables having variances \(\sigma_x^2, \sigma_y^2 \:and\:\sigma_z^2\) respectively, then the correlation between X + Y and Y + Z is:
If X ∼ N (0, 1) and Y = X2 then the correlation coefficient r (X, Y) is
Calculate the correlation coefficient between the following values :
x: 3, 5, 1, 7, 5
y: 4, 3, 0, 8, 2
Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is _______ (round off to 2 decimal places).
