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Is it a good idea to use scatter diagrams to determine if two variables are linearly related?

1) True
2) False

Answer :

Final answer:

Yes, scatter diagrams are effective for determining if two variables are linearly related by visually assessing the pattern of data points and fitting a line of best fit to analyze the relationship and calculate the correlation coefficient. So, 1) True is the correct option.

Explanation:

It is indeed a good idea to use scatter diagrams to determine if two variables are linearly related. The process involves plotting a scatter diagram with one variable on each axis, fitting a line through the data points, and then assessing the pattern. A key indicator of a linear relationship is if you can draw a straight line, known as the line of best fit, through the data points that captures the overall trend of the relationship. When analyzing a scatter plot, you should:

  1. Look for whether the relationship between variables appears to be positive or negative. A positive relationship means that as one variable increases, the other tends to increase as well. A negative relationship indicates that as one variable increases, the other tends to decrease.
  2. Determine if the relationship is linear (points form a pattern close to a straight line) or non-linear (the points do not fit well to a straight line).

Statistical tools like regression analysis and calculating the correlation coefficient help quantify the strength and direction of the relationship. The closer the correlation coefficient is to +1 or -1, the stronger the linear relationship between the variables. In conclusion, scatter plots are useful in identifying the type of relationship between two variables and are especially helpful when assessing the potential for linear regression modeling.

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