Scatter plots. 2) Students predict correlation of linear regression through word problems, graphs, and calculator
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1 Scatter plots 1) Students graph scatter plots 2) Students predict correlation of linear regression through word problems, graphs, and calculator Susan Blakely EPISD Coronado High School (use granted for educational purposes only) September 2010 Lesson objectives Teachers' notes Subject: Topic: Grade(s): Prior knowledge: Cross curricular link(s): Math Algebra 1 9 How to graph coordinates Economics Lesson notes: This lesson activity focuses on students' knowledge of how to graph scatter plots and predict correlations Page 5 Objects are linked to word correlation problems. Touch object and predict correlation. Move the box to check to see if correct. Touch the same link as before to get back to page 5. Test yourself link gives a short quiz on correlations. Touch under question and answer will fade in. Advance page and finish presentation. (Note: Scatter plots w/ calculator is an available notebook file to show correlation on calculator) Lesson objectives Teachers' notes 1
2 Scatter plots are similar to line graphs in that each graph uses the horizontal ( x ) axis and vertical ( y ) axis to plot data points. Scatter plots are most often used to show correlations or relationships among data. Vocabulary Words: scatter plot - shows relationships between two sets of data correlation the relationship between two variables line of best fit (trend line) positive correlation the data displayed on the graph resembles a line rising from left to right negative correlation is a line that best represents the data on a scatter plot the data displayed on the graph resembles a line falling from left to right no correlation the data displayed on the graph neither resembles a line rising nor falling from left to right 2
3 A Correlation can be Predicted without Having to Observe the Data in a Table or Graph. Given the examples, what is the correlation? (positive, negative, or no correlation) Pick a Picture Test Yourself Your grade point average and the number of A s you receive. Correct Positive Negative Time spent studying and the grade on your test. Correct Positive Negative 3
4 The size of a person and the number of fingers he has Positive Negative Correct The weight and height of each member of a soccer team. Correct Positive Negative... 4
5 The size of a car or truck and the number of miles per gallon of gasoline it can travel. Positive Negative Correct The number of telephones using the same cell phone number and the number of calls you receive. Positive Negative Correct 5
6 The speed of a runner and the number of races he/she wins. Correct Positive Negative Test Yourself...write these down & answer Do the data sets have a positive, negative, or no correlation? 1. The minimum wage and the year positive 2. The amount of precipitation and the day of the week no correlation 3. The amount of germs on your hands and the number of times you wash your hands in a day negative 6
7 Correlation can also be shown in scatter plot using graphs for visual reference. A trend line can be shown which is the line of best fit through the data points. Correlation as one data set changes, the other changes. Positive correlation; both data sets increase together. No correlation; as one data set increases, the other decreases. Negative correlation; as one data set increases, the other decreases. 7
8 Use the given data to make a scatter plot of the weight and height of each member of a soccer team. Height (in) Weight (lbs) Weight The points on the scatter plot are (63, 125), (67, 156), (69, 175), (68, 135), and (62, 120) Height Correlation can also be shown in a calculator as a linear regression. Looking at the "r" value, you can determine how close a correlation of the scatter plot. r is the correlation coefficient r 2 is the coefficient of determination 8
9 Correlation Coefficient Relationship Between X & Y "r" Value Interpretation r = Strong Positive As X goes up, Y always also goes up r = Weak Positive As X goes up, Y tends to usually also go up r = 0 No Correlation X and Y are not correlated r = 0.5 Weak Negative As X goes up, Y tends to usually go down r = 1.0 Strong Negative As X goes up, Y always goes down 9
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