Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 164.2 + 4.4 Linear and Quadratic RegressionChapter 4 Sections 2 and 4: Linear and Quadratic RegressionIn this section, we will…Draw and interpret scatterplotsDetermine which regression model is appropriateUse the TI to find the best-fit regression equationInterpret the regression equationMake predictions using the regression equation4.2 + 4.4 Linear and Quadratic RegressionRegression is a process used to relate two quantitative variables.• independent variable: the x variable (or explanatory variable)• dependent variable: the y variable Example: Determine the independent variable and the dependent variable for each of the following.• test score and amount of time spent studying• crime rate and number of police on patrol4.2 + 4.4 Linear and Quadratic RegressionA scatterplot (or scatter diagram) is used to plot two sets of data to see whether a connection or correlation can be established between them.We will interpret scatterplots by identifying their:• form: the function that best describes the relationship between two variables (such as linear, quadratic, cubic, exponential)• direction (linear models only): positive or negative and matches slope4.2 + 4.4 Linear and Quadratic RegressionWe will interpret scatterplots by identifying their:• outliers: any values that do not follow the general pattern of the data• strength: how closely the points in the data match the form4.2 + 4.4 Linear and Quadratic RegressionWe will use the TI to graph our scatterplot and to calculate the regression equation of best fit; refer to your TI regression handout for instructions. • Making predictions: We should only use the regression equation to make predictions for values of x between the smallest and largest x-values in the data set. • Interpreting the slope: the amount of change in y when x increases by 1 unit• Interpreting the y-intercept: the value of y when x = 04.2 + 4.4 Linear and Quadratic RegressionExample #1: The data given represent the t-shirt price (in dollars) and t-shirt sales (number of t-shirts sold) for the Quahog Clothing Boutique.1. Identify the dependent variable and the independent variable.2. Use your calculator to sketch a scatterplot for the data; include your viewing window and scale.4.2 + 4.4 Linear and Quadratic RegressionPrice Sales3 245 187 158 219 1213 1515 918 63. Interpret the scatterplot by describing/identifying each of the following:form:direction:outliers:strength:4. Find the equation of best fit for the data and sketch your best-fit equation over your scatterplot.4.2 + 4.4 Linear and Quadratic Regression5. For what values can we use this regression equation to make predictions?6. Use the regression equation to predict how many t-shirts this store should expect to sell if the price per t-shirt is $10.7. Write a sentence in the context of this scenario that interprets the value of the slope of the regression line.4.2 + 4.4 Linear and Quadratic RegressionExample #2: The data given represent the length of long-distance phone calls (in minutes) and the phone bills (in dollars) for a particular customer.1. Identify the dependent variable and the independent variable.2. Use your calculator to sketch a scatterplot for the data; include your viewing window and scale.4.2 + 4.4 Linear and Quadratic RegressionLength of CallPhone Bill200 50235 60250 62260 68262 63280 65300 63305 71320 70325 72350 75352 783. Interpret the scatterplot by describing/identifying each of the following:form:direction:outliers:strength:4. Find the equation of best fit for the data and sketch your best-fit equation over your scatterplot.4.2 + 4.4 Linear and Quadratic Regression5. Should we use this regression equation to predict the phone bill amount for a phone call lasting 45 minutes? If yes, use your regression equation to predict the phone bill amount for a phone call lasting 45 minutes. If no, explain why not.6. Should we use this regression equation to predict the phone bill amount for a phone call lasting 290 minutes? If yes, use your regression equation to predict the phone bill amount for a phone call lasting 290 minutes. If no, explain why not.7. Write a sentence in the context of this scenario that interprets the value of the slope of the regression line.8. Write a sentence in the context of this scenario that interprets the value of the y-intercept of the regression line.4.2 + 4.4 Linear and Quadratic RegressionExample #3: Because under-inflated or over-inflated tires can increase tire wear, a new tire was tested for wear at different tire pressures. The data below represent the pressure (in pounds per square inch) and mileage (in thousands of miles) obtained in a test of new tires.1. Identify the dependent variable and the independent variable.2. Use your calculator to sketch a scatterplot for the data; include your viewing window and scale.4.2 + 4.4 Linear and Quadratic RegressionPressure Mileage28 4530 5232 5534 5136 473. Interpret the scatterplot by describing/identifying each of the following:form:direction:outliers:strength:4. Find the equation of best fit for the data and sketch your best-fit equation over your scatterplot.4.2 + 4.4 Linear and Quadratic Regression5. For what values can we use this regression equation to make predictions?6. Should we use this regression equation to predict the mileage for a car with a tire pressure of 31.5 pounds per square inch? If yes, use your regression equation to predict the mileage for a car with a tire pressure of 31.5 pounds per square inch. If no, explain why not.7. Should we use this regression equation to predict the mileage for a car with a tire pressure of 25 pounds per square inch? If yes, use your regression equation to predict the mileage for a car with a tire pressure of 25 pounds per square inch. If no, explain why not.8. According to the regression equation, what tire pressure yields the highest mileage?4.2 + 4.4 Linear and Quadratic RegressionIndependent Practice You learn math by doing math. The best way to learn math is to practice, practice, practice. The assigned homework examples provide you with an opportunity to practice. Be sure to complete every assigned problem (or more if you need additional practice). Check your answers to the odd-numbered problems in the back of the text to see whether you have correctly solved