Unit 5: Scatter Plots and Data Analysis Vocabulary
U5 L1: Data Modeling
- Meaning: The process of creating a model that represents the relationship between variables using data.
- Description: Data modeling involves creating mathematical equations or visual representations to understand patterns and relationships in data.
- Picture: [Insert diagram showing a model with variables and a graph]
U5 L2: Bivariate Data
- Meaning: Data that involves two different variables.
- Description: Bivariate data is analyzed to see how two variables relate to one another, often visualized with scatter plots.
- Picture: [Insert example of a scatter plot showing two variables]
U5 L2: Scatter Plot
- Meaning: A graph that displays two quantitative variables on a Cartesian plane.
- Description: Each point represents an observation with an x (independent variable) and a y (dependent variable) value.
- Picture: [Insert a scatter plot example]
U5 L2: Outlier
- Meaning: A data point that differs significantly from other observations.
- Description: Outliers can skew the results of data analysis and may indicate variability in measurement or experimental errors.
- Picture: [Show a scatter plot with an outlier marked]
U5 L2: Clustering
- Meaning: When data points are grouped closely together in a scatter plot.
- Description: Clustering indicates a potential association between the variables and helps identify patterns.
- Picture: [Insert scatter plot with highlighted clusters]
U5 L5: Linear/Nonlinear Association
- Linear Association: When the data points in a scatter plot can be approximated by a straight line. There is a consistent increase or decrease between variables.
- Nonlinear Association: When the data points form a curve or another non-linear form and cannot be well represented by a straight line.
U5 L5: Association/Correlation
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Positive Correlation: As one variable increases, the other also increases.
- Picture: [Insert scatter plot illustrating positive correlation]
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Negative Correlation: As one variable increases, the other decreases.
- Picture: [Insert scatter plot illustrating negative correlation]
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No Correlation: There is no discernible pattern in the relationship between the two variables.
- Picture: [Insert scatter plot illustrating no correlation]
U5 L5: Qualitative Variable
- Meaning: A variable that categorizes or describes an attribute or characteristic.
- Description: Qualitative variables are non-numerical and often represent categories, such as color or type.
- Picture: [Insert examples of qualitative variables]
U5 L5: Quantitative Variable
- Meaning: A variable that can be measured and expressed numerically.
- Description: Quantitative variables can be discrete (countable values) or continuous (measurable values).
- Picture: [Insert examples of quantitative variables]
U5 L5: Line of Best Fit
- Meaning: A straight line that best represents the data on a scatter plot.
- Description: The line minimizes the distance between itself and all the data points, providing a way to predict values.
- Picture: [Insert graph showing a line of best fit through a scatter plot]
U5 L6: Interpreting Key Points of Trend Lines
- Y-Intercept: The value of y when x = 0; represents the starting point of the trend line.
- X-Intercept: The value of x when y = 0; can indicate when the outcome variable is expected to reach zero.
U5 L6: Inference
- Meaning: Drawing conclusions about a population based on sample data.
- Description: Inference involves making predictions or generalizations based on the observed data.
U5 L7: Interpreting the Slope of a Trend Line or Line of Best Fit
- Meaning: The slope indicates the rate of change in y for a unit change in x.
- Description: A positive slope indicates a positive relationship, while a negative slope indicates a negative relationship.
U5 L7: Extrapolate from a Line of Best Fit
- Meaning: Estimating values outside the range of the data points based on the line of best fit.
- Description: Extrapolation should be done cautiously as it may lead to inaccuracies beyond observed data.
U5 L10: How do you Interpret a Graph?
- Description: Read the axes, identify the variables, look for trends, correlations, and anomalies, and assess the context of the data.
U5 L10: Probabilistic vs Deterministic
- Probabilistic: Outcomes are based on probability; there is uncertainty and variability in predictions.
- Deterministic: Outcomes are fixed and certain; the same input will always produce the same output.
Example of All Work Shown
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Data Modeling: Create a model for the following situation where x is the temperature in degrees and y is the number of ice creams sold.
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Bivariate Data: Collect data on temperature (x) and ice cream sales (y).
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Scatter Plot: Plot the points on a scatter plot with temperature on the x-axis and ice creams sold on the y-axis.
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Outlier: Identify any points that are significantly different from the rest.
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Clustering: Note if data points are clustered in certain temperature ranges.
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Association/Correlation: Analyze and determine if the relationship is positive, negative, or none.
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Line of Best Fit: Draw a line that best fits the data points. Calculate the slope to find the relationship.
Make use of graphs and tables to visualize and support your explanation.