Algebra 1: Scatter Plots and Line of Best Fit

Scatter Plots

• A scatter plot visualizes the relationship between paired data points.
• By plotting coordinates, one can observe potential trends or correlations.

Correlation

• The correlation describes the relationship between two data sets, indicating how they move in relation to one another.

Line of Fit

• A line of fit, or line of best fit, represents the trend of data, indicating either a positive or negative correlation.

Positive Correlation

• In positive correlation, as one variable increases, the other does too, resulting in an upward trajectory on the graph.

Negative Correlation

• Negative correlation occurs when one variable increases while the other decreases, leading to a downward slope.

No Correlation

• No correlation means there is no discernible relationship between the data sets, which cannot be effectively represented by a straight line.

Creating a Scatter Plot

• To create a scatter plot, plot the coordinate points, assess correlation, and draw a line fitting the data, ensuring roughly equal points lie above and below it.

Solving Scatter Plot Equations

• After calculating the slope, use any two points on the line to formulate an equation, ultimately converting it to the slope-intercept form ( y = mx + b ).

Extrapolation

• Extrapolation predicts values outside the original data range by utilizing the established model.

Interpolation

• Interpolation estimates values within the data range using the same model.

Finding Line of Fit on Calculator

• Use a calculator to find the line of fit by entering data into statistical lists, followed by executing a linear regression calculation to derive the equation.

Differentiating Extrapolation and Interpolation

• To distinguish between the two, analyze whether the question involves values within or outside the data range.

Positive Correlation Coefficient (C.C.)

• A positive correlation coefficient indicates a positive relationship, with ( r ) values ranging from 0 to 1; values close to 1 signify stronger correlations.

Negative Correlation Coefficient (C.C.)

• A negative correlation coefficient reflects a negative relationship, with ( r ) values spanning from -1 to 0; values closer to -1 show stronger negative correlations.

Correlation Coefficient

• The correlation coefficient, denoted as ( r ), quantifies the strength and direction of a linear relationship between two variables.

Solving Correlation Coefficient Equations

• To solve for correlation coefficients, calculate the line of fit using a calculator, balance ( r ) values according to correlation strength, and compare between variables.

Causation

• Causation refers to a scenario where one variable directly influences another; for instance, more hours worked results in higher pay.