Since the trend is that when the $ x$-values go up, the $ y$-values also go up, we call this a positive correlation, and the correlation coefficient is positive. Thus, if we were to try to fit a line through the points, which is a statistical calculation that finds the “closest” line to the points, it would have a positive slope. Notice from the scatter plot above, generally speaking, the friends who study more per week have higher GPAs. A scatter plot is just a graph of the $ x$-points (number of hours studying each week) and the $ y$-points (grade point average): To make more sense of the data, let’s first order it by the number of hours of studying: Friend It seems like the two variables would be related, but suppose you survey some of your friends to see what a graph would look like: As an example of interpreting sets of data, we may want to see if there is some sort of connection between two sets of data, such as the number of hours studied per week versus grade point average. In the real world, there are always sets of data that need to be interpreted. These include Scatter Plots, Correlation, and Regression, including how to use the Graphing Calculator. Usually around the time that you are beginning “Algebra II” you’ll have another lesson on a little more advanced Statistics than you had earlier (in the Introduction to Statistics and Probability section). Using Graphing Calculator to Get Line of Best Fit Applications of Integration: Area and Volume.Exponential and Logarithmic Integration.Riemann Sums and Area by Limit Definition.Differential Equations and Slope Fields.Antiderivatives and Indefinite Integration, including Trig.Derivatives and Integrals of Inverse Trig Functions.Exponential and Logarithmic Differentiation.Differentials, Linear Approximation, Error Propagation.Curve Sketching, Rolle’s Theorem, Mean Value Theorem.Implicit Differentiation and Related Rates.Equation of the Tangent Line, Rates of Change.Differential Calculus Quick Study Guide. Polar Coordinates, Equations, and Graphs.Law of Sines and Cosines, and Areas of Triangles.Linear, Angular Speeds, Area of Sectors, Length of Arcs.Conics: Part 2: Ellipses and Hyperbolas.Graphing and Finding Roots of Polynomial Functions.Graphing Rational Functions, including Asymptotes.Rational Functions, Equations, and Inequalities.Solving Systems using Reduced Row Echelon Form.The Matrix and Solving Systems with Matrices.Advanced Functions: Compositions, Even/Odd, Extrema.Solving Radical Equations and Inequalities.Solving Absolute Value Equations and Inequalities.Imaginary (Non-Real) and Complex Numbers.Solving Quadratics, Factoring, Completing Square.Introduction to Multiplying Polynomials.Scatter Plots, Correlation, and Regression.Algebraic Functions, including Domain and Range.Systems of Linear Equations and Word Problems.Introduction to the Graphing Display Calculator (GDC).Direct, Inverse, Joint and Combined Variation.Coordinate System, Graphing Lines, Inequalities.Types of Numbers and Algebraic Properties.Powers, Exponents, Radicals, Scientific Notation.
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