Mth 65 Summer 2013 Module 2 Sections 2.4, 2.5, and 2.6. Positive correlation Negative correlation No correlation

Transcription

1 Section 2.4 Scatter Plots and Trend Lines The definition of a Scatter Plot is on page 65. The definition of Correlation is on page 67. Positive correlation Negative correlation No correlation A Trend Line is defined on page 72. Good Trend lines Bad Trend lines Create a scatter plot for the following data table displaying the temperature of a cup of apple juice placed in a freezer. Time (minutes) Temperature ( o F) Don t forget to label and scale your axes. What kind of correlation does the scatter plot you drew for the temperature of the apple juice placed in a freezer display? Draw a trend line on your scatter plot for the temperature of the apple juice placed in a freezer. About half of the data points (not on the line) should be above the line and the other half below the line, all as close to your trend line as possible. Choose two points on the line you drew and find the slope (including units) of your trend line. Then find the equation of your trend line by computing b or substituting into point-slope form. Give your answer in slope-intercept form. slope = equation 1

2 Tuition at Linn-Benton Community College from Fall 2000 to Winter 2013 Actual Year Years since 2000 $ Cost per Credit Draw a scatter plot of the data. Questions to consider before you label and scale on each axis: Which is the independent variable (always displayed on the horizontal axis)? Which is the dependent variable (always displayed on the vertical axis? What type of scale would be appropriate for each axis? What kind of correlation does your scatter plot have? Positive Negative None Draw a trend line that follows the trend of the data. About half of the data points (not on the line) should be above the line and the other half below the line, but not clustered together at the left or right, with as many points as possible close to the trend line. Select two point on the line you drew that you can identify the coordinates for (they do not have to be points from the data set). Find the slope of your trend line. Be sure to include units. Next, find the equation of your trend line in slope-intercept form (, ) (, ) Examine your graph. To the nearest dollar what will the cost per credit be in 2018? 2

3 Section 2.5 Regression Lines Deciding where to draw a trend line by sight does not give a consistent line of best fit. Where the line is drawn varies by each person. There is a complicated method of calculation to find the equation of the best fit line or regression line. So for our purposes in this class, we will use the STAT feature on our TI-83 or TI-84 calculator. The process is detailed on pages 84 through 88 in your textbook. Once we have the equation we can use it to interpret data and predict results. Let s use our tuition data from the notes for 2.4 to explore this process First enter this data in list 1 and list 2. (See pages 83 and 84) Tuition at Linn-Benton Community College from Fall 2000 to Winter 2013 Year $ Cost per Credit ) Enter the years as Years since 2000 as we did on our by hand graph in list 1. 2) Enter the cost per credit in list 2. 3) Create a scatter plot on your calculator using Stat Plot and an appropriate window. (See page 85) 4) Follow the directions on pages 86 and 87 to find the regression line equation. If the correlation coefficient, r, is missing see the top of page 87 and follow the process on page 86 again. The closer your r value is to 1(if the slope is positive) or -1(if the slope is negative), the better this regression line fits the data. What is r s value? How well does your regression line fit the data? Write the equation you found.. Enter this equation into your y= menu and graph to see both you scatter plot and your regression line. What does our regression equation predict that the cost per credit will be at LBCC in 2018? 3

4 Section Using Dimensional Analysis to Solve Applications Dimensional Analysis 1 - Review of Fractions We use these two ideas along with unit fractions (fractions equal to 1). 12 in = 1 ft 1 hr = 60 min 1 lb = 16 oz 1m = 100 cm If you know how two units of measure are related, you can write a unit fraction. Included in your packet is a measurement and conversion table. This table will also be attached to your Mod2 test. The Key the Dimensional Analysis is choosing the appropriate unit fraction. Instead of figuring out whether you want to multiply or divide by the relationship between two units of measure, we will always multiply by a unit fraction that allows us to CANCEL LABELS to achieve the desired unit of measure. 27 ft = yd Convert 3.47 meters to centimeters liters = gallons 4200 kg = oz Dimensional Analysis with Units of Area and Volume How many square centimeters are in a square meter? Notice the exponent on the unit of measure tells you how many times to use the conversion factor. 4

5 How many square inches are in a rectangle with a length of 8 feet and a width of 3 feet? How many cubic inches are in 2.5 cubic feet? 2.5 liters = in 3 6 mi 2 = km 2 Dimensional Analysis with Rates of Change This process usually requires changing units in both the numerator and denominator. Bob walks at 5 miles per hour (mph). What is his speed in meters per second (m/sec)? Change 12 ft 3 /sec to gal/day 5