Regression. Regents Exam #6

Transcription

1 Name: Regression 1 The accompanying table shows the enrollment of a preschool from 1980 through Write a linear regression equation to model the data in the table. 3 The number of newly reported crime cases in a county in New York State is shown in the accompanying table. Write the linear regression equation that represents this set of data. (Let x 0 represent 1999.) Using this equation, find the projected number of new cases for 2009, rounded to the nearest whole number. 2 The data table below shows water temperatures at various depths in an ocean. Write the linear regression equation for this set of data, rounding all values to the nearest thousandth. Using this equation, predict the temperature (ºC), to the nearest integer, at a water depth of 255 meters. 1

2 4 In a mathematics class of ten students, the teacher wanted to determine how a homework grade influenced a student s performance on the subsequent test. The homework grade and subsequent test grade for each student are given in the accompanying table. 5 A real estate agent plans to compare the price of a cottage, y, in a town on the seashore to the number of blocks, x, the cottage is from the beach. The accompanying table shows a random sample of sales and location data. Write a linear regression equation that relates the price of a cottage to its distance from the beach. Use the equation to predict the price of a cottage, to the nearest dollar, located three blocks from the beach. a Give the equation of the linear regression line for this set of data. b A new student comes to the class and earns a homework grade of 78. Based on the equation in part a, what grade would the teacher predict the student would receive on the subsequent test, to the nearest integer? 6 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. The accompanying table shows the day, x, and the number of sheets in stock, f(x). Write the linear regression equation for this set of data, rounding the coefficients to four decimal places. Use this equation to determine the day the sheets will be shipped. 2

3 7 The accompanying table shows the percent of the adult population that married before age 25 in several different years. Using the year as the independent variable, find the linear regression equation. Round the regression coefficients to the nearest hundredth. Using the equation found above, estimate the percent of the adult population in the year 2009 that will marry before age 25, and round to the nearest tenth of a percent. 9 A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over a 10-minute period. Write an exponential regression equation for the data, rounding all values to the nearest thousandth. 8 The mid-september statewide average gas prices, in dollars per gallon, (y), for the years since 2000, (x), are given in the table below. 10 The table below shows the concentration of ozone in Earth s atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. Write a linear regression equation for this set of data. Using this equation, determine how much more the actual 2005 gas price was than the predicted gas price if the actual mid-september gas price for the year 2005 was $

4 11 The table below shows the number of new stores in a coffee shop chain that opened during the years 1986 through 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. Using x 1 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. 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. 13 The data collected by a biologist showing the growth of a colony of bacteria at the end of each hour are displayed in the table below. Write an exponential regression equation to model these data. Round all values to the nearest thousandth. Assuming this trend continues, use this equation to estimate, to the nearest ten, the number of bacteria in the colony at the end of 7 hours. 4

5 14 The table below shows the results of an experiment involving the growth of bacteria. 16 Water is draining from a tank maintained by the Yorkville Fire Department. Students measured the depth of the water in 15-second intervals and recorded the results in the accompanying table. Write a power regression equation for this set of data, rounding all values to three decimal places. Using this equation, predict the bacteria s growth, to the nearest integer, after 15 minutes. 15 The accompanying table shows the number of new cases reported by the Nassau and Suffolk County Police Crime Stoppers program for the years 2000 through Write the power regression equation for this set of data, rounding all values to the nearest ten thousandth. Using this equation, predict the depth of the water at 2 minutes, to the nearest tenth of a foot. If x 1 represents the year 2000, and y represents the number of new cases, find the equation of best fit using a power regression, rounding all values to the nearest thousandth. Using this equation, find the estimated number of new cases, to the nearest whole number, for the year The accompanying table shows wind speed and the corresponding wind chill factor when the air temperature is 10ºF. 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? 5

6 ID: A Regression Answer Section 1 ANS: y 1.08x 2125 REF: b 2 ANS: y 0.112x (255) REF: b 3 ANS: y 35.5x 457.5, 103 REF: b 4 ANS: y x , 80 REF: b 5 ANS: y x , 209,090 REF: b 6 ANS: y x , 14 REF: b 7 ANS: y 0.58x , 19.9 REF: b 8 ANS: y x 1.259, ANS: y (0.954) x 10 ANS: y 0.488(1.116) x 11 ANS: y (1.586) x REF: b REF: a2 REF: a2 REF: a2 1

7 ID: A 12 ANS: y (1.1509) x. y (1.1509) REF: a2 13 ANS: y (1.652) x (1.652) REF: a2 14 ANS: y 2.001x 2.298, 1,009 REF: fall0938a2 15 ANS: y x 0.243,272 REF: b 16 ANS: y x , 4.9 REF: b 17 ANS: y lnx, 16, 6 PTS: 6 REF: b 2