Name: _____________________________ Date: _____________ Mr. Nickels Math 3C Regressions HW 1) 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. A. Write a linear regression equation that relates the price of a cottage to its distance from the beach. B. Use the equation to predict the price of a cottage, to the nearest dollar, located three blocks from the beach. 2) Jean invested $380 in stocks. Over the next 5 years, the value of her investment grew, as shown in the accompanying table. A. Write the exponential regression equation for this set of data, rounding all values to two decimal places. B. Using this equation, find the value of her stock, to the nearest dollar, 10 years after her initial purchase. 3) Which scatter diagram shows the strongest positive correlation? 4) A box containing 1,000 coins is shaken, and the coins are emptied onto a table. Only the coins that land heads up are returned to the box, and then the process is repeated. The accompanying table shows the number of trials and the number of coins returned to the box after each trial. A. Write an exponential regression equation, rounding the calculated values to the nearest ten-thousandth. B. Use the equation to predict how many coins would be returned to the box after the eighth trial. 5) The relationship of a woman’s shoe size and length of a woman’s foot, in inches, is given in the accompanying table. The linear correlation coefficient for this relationship is (1) 1 (3) 0.5 (2) –1 (4) 0 6) Which graph represents data used in a linear regression that produces a correlation coefficient closest to –1? 7) What could be the approximate value of the correlation coefficient for the accompanying scatter plot? (1) -0.85 (2) -0.16 (3) 0.21 (4)0.90 8) The table below shows the results of an experiment involving the growth of bacteria. A. Write a power regression equation for this set of data, rounding all values to three decimal places. B. Using this equation, predict the bacteria’s growth, to the nearest integer, after 15 minutes. 9) 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 2002. A. 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. B. Using this equation, find the estimated number of new cases, to the nearest whole number, for the year 2007. C. Using this equation, find the estimated number of new cases, to the nearest whole number, for the year 2014. 10) The accompanying table shows wind speed and the corresponding wind chill factor when the air temperature is 10ºF. A. Write the logarithmic regression equation for this set of data, rounding coefficients to the nearest ten thousandth. B. Using this equation, find the wind chill factor, to the nearest degree, when the wind speed is 50 miles per hour. C. Based on your equation, if the wind chill factor is 0, what is the wind speed, to the nearest mile per hour?