Correlation Relationship between two variables in a scatterplot. As the x values go up, the y values go up. As the x values go up, the y values go down. There is no relationship between the x and y values as the x values go up. Correlation is measured by a correlation coefficient represented by the letter "r". Need to be able to do on TN Ready: 1. Interpret the correlation coefficient. 2. Compare correlation coefficients. 3. Recognize how it would change (increase/ decrease) if given more data point(s).
Positive Correlation Shown on a scale between 0 and 1 (r value) Perfect positive linear correlation = line = 1 No correlation = 0 Strong positive correlation if r > 0.50 Weak positive correlation if r < 0.50 Positive Correlation Scale Weak Positive Strong Positive 0 No Correlation 0.5 1 Perfect Positive Linear Correlation
Negative Correlation Shown on a scale between 1 and 0 (r value) Perfect negative linear correlation = line = 1 No correlation = 0 Strong negative correlation if r < 0.50 Weak negative correlation if r > 0.50 Negative Correlation Scale Strong Negative Weak Negative 1 Perfect Negative Linear Correlation 0.5 0 No Correlation
Correlation Scale Strong Negative Weak Negative Weak Positive Strong Positive 1 Perfect Negative Linear Correlation 0 No Correlation 1 Perfect Positive Linear Correlation Which is a stronger correlation coefficient? 0.8 or 0.6
Which is a stronger correlation coefficient? 0.73 or 0.699 Which correlation coefficient indicates the strongest relationship between two random variables for a fixed sample size? A) 0.78 B) 0.59 C) 0.65 D) 0.89
r =.9918 What will happen to the correlation coefficient if the blue point is added to the data set (do not include red point)? What will happen to the correlation coefficient if the red point is added to the data set (do not include blue point)?
Correlation vs. Causation Correlation relationship between two variables when one variable increases, the other variable increases or decreases Causation when one variable causes the other variable to happen Correlation does not mean causation!!! Decide whether the following correlated relationships has a causal relationship. 1. The number of cold, snowy days and the amount of hot chocolate sold at a ski resort. 2. The number of miles driven and the amount of gas used. 3. The amount of cars a salesperson sells and how much commission he makes. 4. The number of cars traveling over a busy holiday weekend and the number of accidents reported. 5. The annual salary and blood pressure for men ages 20 60.
Line of Best Fit A straight line or equation that best represents the data on a scatter plot. This line may pass through some, none, or all of the points. Questions about line of best fit may include finding the best answer choice for the line of best fit, predicting values, and finding residuals. Finding Line of Best Fit Used to teach students how to find line of best fit in their calculators. TN Ready assessment questions don't require you to find the equation of the line of best fit, you just need to pick which equation best fits.
Approach to answering Line of Best Fit questions 1. See what type of slope the scatter plot data shows and eliminate any incorrect possibilities. 2. Approximate the y intercept and see if any of the answer choices are not reasonable. 3. Look at the slope of the remaining possibilities and see which one makes the most sense. Which of the following equations best represents the line of best fit for the data shown in the scatterplot below?
Which scatter plot would a line of best fit 1 be described by the equation, y = x + 2? 2 Which equation best fits the scatter plot shown below?
Predicting using the Line of Best Fit You may be asked to predict an amount that is not given. This amount is not what is guaranteed what the value will be, but it is based on the data that has been collected already. The line of best fit will be given in the problem and the question will give an x or y value. Input the x or y value into the equation. Residuals A residual is the difference between the actual point on the scatter plot and the predicted value (the point on the line of best fit). RESIDUAL = ACTUAL EXPECTED
Graphs of Residuals The graph of residuals is the same graph of the scatterplot, except the line of best fit becomes the x axis. If the point was above the line of best fit, the y value in the residuals graph will be positive. If the point was below the line of best fit, the y value in the residuals graph will be negative. Scatter plot w/ line of best fit Residual plot