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Algebra 2 – Statistics Day 1 Name ____________________________________ Date _______________REGRESSION: CURVES OF BEST FIT WITH YOUR GRAPHING CALCULATORSketch a scatterplot with the following characteristics: Positive Linear Correlation Negative Linear Correlation Exponential Correction Logarithmic Correlation Quadratic Correction No Correlation When data is displayed with a ________________, it is often useful to attempt to represent that data with the equation of a line or curve for purposes of predicting values that may not be displayed on the plot.Such a line or curve is called the _______________________________. Equations that represent these curves are called _______________________________equations. We can use these to help us extrapolate the data and predict future outcomes.Circle the following sets of data points that show a strong correlation. Name the curve that best represents this positive or negative correlation. (Choose from line, quadratic, log, or exponential).31102305143500787404191000 ____________ __________ ____________ _____________ ____________ ___________ PRACTICE: Now let’s use our Calculators (STAT key) to put in data and find a regression equation that best fits each model below. Using this equation, we can then make predictions.Ex 1) A rapidly growing bacteria has been discovered.Its growth rate is shown in the chart.Hours since observation beganNumber of bacteria in the sample020140275315042975510a)? First, turn the Stat Plot on (2nd y=, then hit enter). Next, put the chart data in STAT-Edit L1 (1st column) and L2 (2nd column).?Hit Zoom #9 (ZoomStat). Sketch the resulting scatter plot below.b)??Determine which regression model will best approximate your data. (Choose: Linear, quadratic, logarithmic, or exponential) ____________________________c)??Find the regression equation for your model, rounding values to three decimal places. Go to STAT-Calc and scroll down to the type based on your answer from b. Keep hitting Enter. Write down the equation below. y = ______________________________d) Using your regression equation, determine how many bacteria, to the nearest integer, will be present in 12 hours. (Replace x with 12.)EXAMPLE 2: Graph each set of data on your graphing calculator. Decide whether a regression model is reasonable. If so, write the equation of the trend line and predict the y-value when x is equal to 10.{(-2, -3.9), (-1, -1.8), (0, 0.1), (1, 1.9), (2, 3.8)}{(0.3, 0), (0.8, 3), (1.1, 5), (2.0, 6), (2.5, 6)} {(-11, 1), (-7, 0.5), (0, 1.5), (10, 2), (20, 2.5)}EXAMPLE 3: Is there a relationship between the price of a home and its square feet?Hanna Properties specializes in custom-home resales in the Equestrian Estates, an exclusive subdivision in Pheonix, Arizona. A random sample of 9 custom homes currently listed for sale provided the following information on size and price. Here, x denotes size, in hundreds of square feet, rounded to the nearest hundred, and y denotes price, in thousands of dollars, rounded to the nearest thousand. X262733292934304022Y540555575577606661738804496Find the line of best fit.Predict the price of a 2600 sq ft home in the Equestrian Estates.EXAMPLE 4: The table shows the amount of medicine for treating a disease in the bloodstream over the 9 hours following a dose of 10 mg.? It seems that the rate of decrease of the drug is approximately proportional to the amount remaining. Time(hrs)Drug Amount(mg)01018.327.236.045.054.463.772.882.5What function best models this data? (Look at the graph) Write the regression equation.b.) Using your equation, about how much of the medicine is in the patient's bloodstream after 12 hours?EXAMPLE 5: A factory is producing and stockpiling metal sheets to be shipped to an automobile manufacturing plant.? The factory ships only when there is a minimum of 2,050 sheets in stock at the beginning of that day.? The table shows the day,?x, and the number of sheets in stock,?f?(x),at the beginning of that day.a.) Write a linear regression equation for this set of data, rounding coefficients to two decimal places.b.)? Use this equation to determine the day the sheets will be shipped.DaySheets in Stock18602930310004115051200613606. Is there a relationship between the fat grams and the total calories in fast food? Can we predict the number of total calories based upon the total fat grams? 0508000SandwichTotal Fat (g)Total CaloriesHamburger9260Cheeseburger13320Quarter Pounder21420Quarter Pounder with Cheese30530Big Mac31560Arch Sandwich Special31550Arch Special with Bacon34590Crispy Chicken 25500Fish Fillet 28560Grilled Chicken20440Grilled Chicken Light5300Find the line of best fit.Predict the total calories based on 22 grams of fat.7. The table shows the percentage of the population not covered by health insurance in selected states for the years 1990 and 1999.StateIdahoIllinoisMichiganMontanaNew York199015.110.99.414.012.1199919.114.111.218.616.4Use your graphing calculator to draw a scatterplot showing the relationship between the percentage not covered by health insurance in 1990 and the percentage not covered in 1999. Use the 1990 percentage as the independent variable. What type of relationship is shown?What is the line of best fit?In Wyoming, 12.5% of the population was not covered by health insurance in 1990. Use your model to estimate the percentage that was not covered in 1999.The actual percentage for Wyoming in 1999 was 16.1. Is your model reasonable?8. Graph each set of data on your graphing calculator. Decide whether a regression model is reasonable. If so, write the equation of the trend line and predict the y-value when x is equal to 10.{(5, 4), (25, 6), (-4, 3), (-5, -10), (-25, 100), (50, -25)}{(1, 2.1), (3, 3.1), (5, 4.0), (7, 5.2), (9, 5.9)}{(2, 3.5), (4, 4.9), (6, 6.3), (8, 4.6), (10, -2.9), (0, 15)}{(-38, 2104), (-22, 888), (-4, 132), (10, -8), (25, 277), (40, 1012)}{(-15,-0.005 ), (-10, -0.05), (-5, -0.5), (0, -3), (5, -25), (10, -175), (15, -1300)}9a. What regression model would be appropriate for the following set of data? What is the regression equation? (Hint-Determine the x and y values from the graph, input the values into the list function and use the STAT CALC function on your graphing calculator to find the regression equation.)9b. Predict the value of y when x is 100.3966210177800010. The accompanying table shows wind speed and the corresponding wind chill factor when the air temperature is 10?F. Write the logarithmic regression equation for this set of data, rounding coefficients to the nearest ten thousandth. Using this equation, find the wind chill factor, to the nearest degree, when the wind speed is 50 miles per hour. Based on your equation, if the wind chill factor is 0, what is the wind speed, to the nearest mile per hour? Sketch the scatterplot.4018280444500011. A population of single-celled organisms was grown in a Petri dish over a period of 16 hours. The number of organisms at a given time is recorded in the table below. Determine the exponential regression equation model for these data, rounding all values to the nearest ten-thousandth. Using this equation, predict the number of single-celled organisms, to the nearest whole number, at the end of the 18th hour. Sketch the scatterplot.51060351441450012. The table below shows the number of new stores in a coffee shop chain that opened during the years 1986 through 1994. Using to represent the year 1986 and y to represent the number of new stores, write the exponential regression equation for these data. Round all values to the nearest thousandth. ................
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