Exploring Linear Relationships in Scatter Plots

A scatter plot shows a linear relationship between the number of hours studied and the test scores. Which of the following best describes the line of best fit?

• A line that passes through all the data points.

• A line that minimizes the distance between the line and all the data points.

• A line that is parallel to the x-axis.

• A line that is parallel to the y-axis.

Which of the following scatter plots suggests a strong positive linear association?

• A scatter plot where points are widely scattered with no clear pattern.

• A scatter plot where points form a downward trend.

• A scatter plot where points are closely clustered around an upward sloping line.

• A scatter plot where points form a horizontal line.

If a scatter plot shows a linear association, what is the purpose of fitting a straight line to the data?

• To make the scatter plot look more organized.

• To predict values and understand the relationship between variables.

• To change the data points.

• To eliminate outliers.

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• 2

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Which of the following statements is true about a scatter plot with a perfect linear association?

• All data points lie exactly on the line of best fit.

• The data points are randomly scattered.

• The line of best fit is horizontal.

• The line of best fit is vertical.

A scatter plot shows a linear association with some outliers. How do outliers affect the line of best fit?

• They have no effect on the line of best fit.

• They can significantly change the slope and position of the line.

• They make the line of best fit vertical.

• They make the line of best fit horizontal.

What does a negative slope in the line of best fit indicate about the relationship between two variables in a scatter plot?

• As one variable increases, the other variable also increases.

• As one variable increases, the other variable decreases.

• There is no relationship between the variables.

• The variables are constant.

Which of the following is NOT a step in informally assessing the fit of a line to a scatter plot?

• Checking the closeness of data points to the line.

• Calculating the exact distance of each point from the line.

• Observing the overall trend of the data.

• Ensuring the line passes through the origin.

• The point where the line crosses the x-axis.

• The point where the line crosses the y-axis.

• The average of the x-values.

• The average of the y-values.

If a scatter plot shows no apparent pattern, what can be said about the relationship between the two variables?

• There is a strong positive linear relationship.

• There is a strong negative linear relationship.

• There is no linear relationship.

• The variables are inversely proportional.