Let Y represent the profit (or loss) for a certain company X years after 1975. Based on the data shown below, a statistician calculates a linear model Y = 2.91X + 45.99. X y 5 30.97 6 29.06 7 25.95 8 23.14 9 18.23 10 16.82 11 15.41 12 10.4 012 Use the model to estimate the profit in 1980 y =

The following table gives estimates of the percent of a certain country's population below the poverty level for 1998–2008. Year Percent 1998 12.8 2000 11.2 2002 12.1 2004 12.7 2006 12.9 2008 13.2 Find the least squares line that relates years to percent below the poverty level. (Let x = 0 represent the year 1998. Enter a mathematical expression.

The percentage of adults who smoke in America is given below. Year America 1970 37.4 mon n 1980 33.2 1990 25.3 2000 23.1 2010 19.4 a) Write the linear regression model for A(x), representing the percentage of adult smokers in America x years since 1970. [Use your calculator OR Desmos to find the equation, Round coefficients to the nearest 100"] b) What is the slope of A(x)? Explain its meaning. c) Solve A(x) = 15. Show your work. Explain the meaning of your answer. d) Suppose in 2005, there were approximately 200 million adults in America. Use your model to estimate how many were smokers. Show how you get your answer.

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The average top ticket price for Broadway musicals has increased dramatically between 1975 and 2003. 1985 1998 2000 2003 72.83 118.97 130.15 44.99 Year Average Ticket Price 1975 13.63 a. Using the data in the table, find the linear regression equation that best fits the data. (Let x = 0 represent the number of years since 1970.) y = (Round values to three decimal places.) b. Predict the average top ticket price for Broadway musicals in the year 2012 if the price continues to increase at the same rate. (Let x represent the number of years since 1970.) (Round to two decimal places.) c. Find the rate at which the price is rising. per year (Round to two decimal places.)