Answer :
Final answer:
A scatter diagram is used in statistics to depict the relationship between two variables. In regression theory, it's used to draw a line of best fit or regression line to estimate the correlation between the variables. The plot's linear trend and coefficient significance assist in predicting future values.
Explanation:
A scatter diagram, or scatter plot, is a type of graphical representation used in statistics. It plots two variables of a set of data on different axes, with one variable on the x-axis and the other on the y-axis. Each point on the plot represents an observation. The pattern of the resultant points can suggest the relationship between the two variables.
In the theory of regression, a scatter diagram plays a crucial role. A scatter diagram is used to identify the type of relationship (if any) between two variables.
The regression line (or line of best fit) can be drawn in the scatter plot to estimate the correlation between variables. This line is the one that fits the data best, minimizing the sum of the squared errors (SSE). This process of fitting the line is known as linear regression.
The correlation coefficient (r) significance and the scatter plot's linear trend help discern the appropriateness of predicting future values within the observed domain. However, the line should not be used for prediction if 'r' is not significant, or if the plot does not show a linear trend.
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