The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. Year Retail Sales 0 85.851 3 108.426 6 141.781 9 169.256 12 202.297 15 222.266 Let S'(t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t) = 9.44t+ 84.182. 220 210- 200 190 180 170 160 150 140 130 120 110 100 90- 804 12 Use the above scatter plot to decide whether the linear model fits the data well. O The function is not a good model for the data The function is a good model for the data. Estimate the retails sales in the U. S. in 2014. 273 x billions of dollars. Use the model to predict the year in which retails sales will be $246 billion. 2015 Situation: The Ipod Touch has been out for two years now and a lot of data has been collected. Relevant Relationship: There is a functional relationship between Price of an IPod Touch,p and Weekly Demand,s. Below is a table of data that have been collected Price,p,($) Weekly Demand,s,(1,000s) 150 170 190 210 230 250 209 205 200 190 178 171 A.. Find the linear model that best fits this data using regression and enter the model below (for entry round the linear parameter value to nearest 0.01 and constant parameter to nearest 1) S = T(p) = B. The squared correlation coefficient r was Select an answer 0.95 (note: values less than 0.95 MAY mean the model is not appropriate for making predictions) Now answer these two questions using the UNROUNDED model parameters C. What does the model predict will be the weekly demand if the price of an ipod touch is $248? (nearest 100) D. According to the model at what should the price be set in order to have a weekly demand of 173,300 ipod Touches? $ (nearest $1) Linear Regression Use linear regression to find the equation for the linear function that best fits this data. Round both numbers to two decimal places. Write your final answer in a form of an equation y=mx+b X 1 2 3 4 5 6 y 88 106 137 148 181 199 Linear Regression Application, Interpolation and Extrapolation Use the data and story to answer the following questions The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. x 11.6 8 6.9 3.7 2.4 2.3 2.3 0.9 y 13.8 11.1 10.2 7.5 5.9 6.3 6.1 4.7 x = thousands of automatic weapons y = murders per 100,000 residents Use your calculator to determine the equation of the regression line. (Round to 2 decimal places) Determine the regression equation in y = ax + b form and write it below. A) How many murders per 100,000 residents can be expected in a state with 3.1 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 2.4 thousand automatic weapons? Answer = Round to 3 decimal places. Based on the data shown below, calculate the correlation coefficient (to three decimal places) x y 4 13.74 5 15.15 6 19.26 7 20.37 8 22.38 9 24.49 10 24.5 11 25.41 12 29.82 13 30.03 14 34.54 The following data includes the year, make, model, mileage (in thousands of miles) and asking price (in US dollars) for each of 13 used Honda Odyssey minivans. The data was collected from the Web site of the Seattle P-I on April 25, 2005. year make model mileage price 2004 Honda Odyssey EXL 20 26900 2004 Honda Odyssey EX 21 23000 2002 Honda Odyssey 33 17500 2002 Honda Odyssey 41 18999 2001 Honda Odyssey EX 43 2001 Honda Odyssey EX 26 17200 67 18995 2000 Honda Odyssey LX 46 13900 2000 Honda Odyssey EX 72 15250 2000 Honda Odyssey EX 82 13200 2000 Honda Odyssey 99 11000 1999 Honda Odyssey 71 13900 1998 Honda 1995 Honda Odyssey Odyssey EX 85 8350 100 5800 Compute the correlation between mileage and price for these minivans. (Assume the correlation conditions have been satisfied and round your answer to the nearest 0.001.) Match each scatterplot shown below with one of the four specified correlations. b 80% a. -0.07 b. -0.79 c. 0.05 d. 0.98 0000 Run a regression analysis on the following bivariate set of data with y as the response variable. X y 63.1 63 66.1 75.9 72.2 79 68.9 84.8 89 92.4 83.7 62.6 85.2 81.9 68.1 80.6 62.5 77 66.5 74.8 81.1 90.8 45.6 42.8 Find the correlation coefficient and report it accurate to three decimal places. r = What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place. (If the answer is 0.84471, then it would be 84.5%...you would enter 84.5 without the percent symbol.) % Based on the data, calculate the regression line (each value to three decimal places) y = x + Predict what value (on average) for the response variable will be obtained from a value of 75.5 as the explanatory variable. Use a significance level of a = 0.05 to assess the strength of the linear correlation. What is the predicted response value? (Report answer accurate to one decimal place.) y = Match each scatterplot shown below with one of the four specified correlations. b C a 8 d a. -0.13 b. -0.25 c. 0.72 d. -0.77 8