2.4 Representing the Relationship Between Two Quantitative Variables

• Data collection involves measuring or recording the numeric values for each variable.
• What are qualitative variables used to represent?

  Observations or categories
• A scatter plot is a graphical tool used to visualize the relationship between two quantitative variables.
• In a scatter plot, the independent variable is plotted on the y-axis.

  False
• Match the trend type with its description:

  Positive Relationship ↔️ One variable increases as the other increases

  Negative Relationship ↔️ One variable increases as the other decreases

  No Relationship ↔️ No clear pattern in the data
• The correlation coefficient ranges from -1 to 1.
• To calculate the correlation coefficient, you need the individual data points, the means of the variables, and the total number of data points.
• What is the final step after identifying two quantitative variables for analysis?

  Gather and organize data
• Match the type of variable with its feature:

  Quantitative Variables ↔️ Numeric data

  Qualitative Variables ↔️ Non-numeric data
• Properly gathering and organizing data is crucial for analyzing the relationship between quantitative variables


  True
• A scatter plot showing height and weight would indicate a positive linear relationship

  True
• Match the type of relationship with its description:

  Positive Relationship ↔️ One variable increases as the other increases

  Negative Relationship ↔️ One variable increases as the other decreases

  No Relationship ↔️ No clear pattern or trend
• What does the trend in a scatter plot describe?

  Overall pattern of data
• Match the type of correlation with its correlation coefficient range:

  Positive Correlation ↔️ 0 < r ≤ 1

  Negative Correlation ↔️ -1 ≤ r < 0

  No Correlation ↔️ r = 0
• A correlation coefficient of 0.8 indicates a strong positive correlation.

  True
• The slope of the regression line represents the average change in y for a one-unit change in x.
• The y-intercept of the line of best fit represents the value of y when x is zero.
• Arithmetic operations are possible with quantitative variables but not with qualitative variables.

  True
• Steps to gather and organize quantitative data:

  1️⃣ Collect data for both variables

  2️⃣ Organize the data in a table
• Gathering and organizing data is crucial for analyzing the relationship between two quantitative variables.


  True
• What are the two steps involved in gathering and organizing quantitative data?

  Collect and organize data
• A scatter plot is a graphical tool used to visualize the relationship between two quantitative variables.
• The overall pattern or direction of data points in a scatter plot is called a trend.
• What does the correlation coefficient measure?

  Strength and direction of relationship
• What is the formula for calculating the correlation coefficient?

  r = \frac{\sum_{i = 1}^{n} (x_{i} - \bar{x})(y_{i} - \bar{y})}{\sqrt{\sum_{i = 1}^{n} (x_{i} - \bar{x})^{2}} \sqrt{\sum_{i = 1}^{n} (y_{i} - \bar{y})^{2}}}</latex>
• Match the type of variable with its feature:

  Quantitative Variables ↔️ Numeric data

  Qualitative Variables ↔️ Non-numeric data
• Arithmetic operations are possible with quantitative variables but not qualitative variables

  True
• Data can be organized in a spreadsheet with variables listed in rows and columns
• A scatter plot represents data points as individual dots
• Scatter plots allow us to visually inspect the trend and strength of the relationship between two quantitative variables


  True
• The correlation coefficient measures the strength and direction of the linear relationship between two quantitative variables


  True
• The correlation coefficient ranges from -1 to 1.
• In a positive correlation, as one variable increases, the other variable increases.
• The equation of the regression line is y = mx + b, where m is the slope and b is the y-intercept.

  True
• What does a positive slope in the line of best fit indicate?

  Positive correlation
• Quantitative variables are measurable characteristics that take numeric values.
• Match the type of data with the corresponding arithmetic operations:

  Quantitative ↔️ Possible

  Qualitative ↔️ Not possible
• Organizing data in a table involves listing one variable in the rows and the other in the columns.
• Why is identifying the two quantitative variables a crucial first step in data analysis?

  To analyze their relationship
• Why is it crucial to properly gather and organize data when analyzing quantitative variables?

  Sets foundation for analysis