Annual high temperatures in a certain location have been tracked for several years. Let X represent the year and Y the high temperature. Based on the data shown below, calculate the regression line (each value to two decimal places). y = X + y 3. 30.56 29.29 27.62 25.15 21.68 8 18.71 18.44 10 13.37 11 11.9 4567 0oc
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- Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Postal RatesThe table below shows the cost s, in cents, of a domestic first-class postage stamp in the United States tyears after 1900. t=time,inyearssince1900 s=costofstamp 19 2 32 3 58 4 71 8 78 15 85 22 95 32 102 37 109 44 116 47 a.Use exponential regression to model s as an exponential function of t. b.What cost does your model give for a 1988 stamp? Report your answer to the nearest cent. The actual cost was 25cents. c.Plot the data and the exponential model.Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Gray Wolves in WisconsinGray wolves were among the first mammals protected under the Endangered Species Act in the 1970s. Wolves recolonized in Wisconsin beginning in 1980.Their population grew reliably after 1985 as follows: Year Wolves Year Wolves 1985 15 1993 40 1986 16 1994 57 1987 18 1995 83 1988 28 1996 99 1989 31 1997 145 1990 34 1998 178 1991 40 1999 197 1992 45 2000 266 a. Explain why an exponential model may be appropriate. b. Are these data exactly exponential? Explain. c. Find an exponential model for these data. d. Plot the data and the exponential model. e. Comment on your graph in part d. Which data points are below or above the number predicted by the exponential model?Special Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Caloric Content Versus Shell Length In 1965, Robert T.Paine gathered data on the length L, in millimeters, of the shell and the caloric content C, in calories, for a certain mollusk. The table below is adapted from those data. L=length C=Calories 7.5 92 13 210 20 625 24 1035 31 1480 a.Find an exponential model of calories as a function of length. b.Plot the graph of the data and the exponential model. Which of the data points show a good deal less caloric content than the model would predict for the given length? c.If length is increased by 1millimeter, how is caloric content affected?
- Special Rounding Instructions. For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Growth in Length of HaddockA study by Raitt showed that the maximum length that a haddock could be expected to grow is about 53centimeters.Let D=D(t) denote the difference between 53centimeters and the length at age t years. The table below gives experimentally collected values for D. Age t Difference D 2 28.2 5 16.1 7 9.5 13 3.3 19 1.0 a.Find an exponential model of D as a function of t. b.Let L=L(t) denote the length in centimeters of a haddock at age t years. Find the model for L as a function of t. c.Plot the graph of the experimentally gathered data for the length L at ages 2,5,7,13, and 19years along with the graph of the model you made for L. Does this graph show that the 5year old haddock is a bit shorter or a bit longer than would be expected? d.A fisherman has caught a haddock that measures 41centimeters. What is the approximate age of the haddock?Remainder Round all answers to two decimal places unless otherwise indicated. Gross Domestic Product U.S. gross domestic product, in trillions of dollars, is given in the table below. Date Gross domestic product 2010 15.0 2011 15.5 2012 16.2 2013 16.7 a.Find the equation of the regression line, and explain the meaning of its slope. Round regression line parameters to two decimal places. b.Plot the data points and the regression line. c.When would you predict that a gross domestic product of 17.3 trillion dollars would be reached? The actual gross domestic product in 2014 was 17.3 trillion dollars. What does that say about your prediction?A Dubious Model of Oil Prices The following table shows the prices of oil in U.S. dollars per barrel, t years since 1990, One analysis involving additional data used a cubic equation to model this data. t Years since 1990 0 2 5 7 10 12 15 17 20 21 P Price, dollars per barrel 18.91 16.22 16.63 18.20 27.04 23.47 49.63 69.04 77.46 106.92 a. Use cubic regression to model these data. Round the regression parameters to four decimal places. b. Plot the data along with the cubic model. c. In the analysis mentioned above, the graph is expanded through 2020. Expand the viewing window to show the model from 1990 to 2020. d. What estimate does the model give for oil prices in 2015? e. The actual price of oil in December of 2015 was about 35 per barrel. What basic principle in the use of models would be violated in relying on the estimate in part d?
- Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Design Patents The following table shows the number P of design patents awarded by the U.S. Patents and Trademark Office from 1950 through 2010. t = years since 1950 P = patents 0 4718 10 2543 20 3214 30 3949 40 8024 50 17,413 60 22,799 a.Use exponential regression to model P as a function of t. b.Plot the data along with the regression equation. c.In what years were there more patents awarded than might be expected from the model?Zipfs Law The following table shows U.S cities by rank in terms of population and population in thousands. City Rank r Population N New York 1 8491 Chicago 3 2722 Philadelphia 5 1560 Dallas 9 1280 Austin 11 913 San Francisco 13 852 Columbus 15 836 A rule known as Zipfs law tells us that it is reasonable to approximate these data with a power function. a Use power regression to express the population as a function of the rank. b Plot the data along with the power function from part a. c Phoenix is the sixth largest city in the United States. Use your answer from part a to estimate population of Phoenix. Round your answer in thousands to the nearest whole number. Note: The actual population is 1537 thousand.Special Rounding Instructions For this exercise set, round all regression parameters to three decimal places, but round all other answers to two decimal places unless otherwise indicated. Atmospheric Pressure The table below gives a measurement of atmospheric pressure, in grams per square centimeter, at the given altitude, in kilometers. Altitude Atmospheric Pressure 5 569 10 313 15 172 20 95 25 52 For comparison, 1 kilometer is about 0.6 mile, and 1 gram per square centimeter is about 2 pounds per square foot. a.Plot the data on atmospheric pressure. b.Make an exponential model for the data on atmospheric pressure. c.What is the atmospheric pressure at an altitude of 30 kilometers? d.Find the atmospheric pressure on Earths surface. This is termed standard atmospheric pressure. e.At what altitude is the atmospheric pressure equal to 25 of standard atmospheric pressure?
- Noise and Intelligibility Audiologists study the intelligibility of spoken sentences under different noise levels. Intelligibility, the MRT score, is measured as the percent of a spoken sentence that the listener can decipher at a cesl4ain noise level in decibels (dB). The table shows the results of one such test. (a) Make a scatter plot of the data. (b) Find and graph the regression line. (c) Find the correlation coefficient. Is a linear model appropriate? (d) Use the linear model in put (b) to estimate the intelligibility of a sentence at a 94-dB noise level.A simple linear regression model was used to describe the relationship between y = hardness of molded plastic and x = amount of time elapsed since the end of the molding process. Summary quantities included n = 16, SSResid = 1235.470, and SSTo = 25,221.368. (a) Calculate an estimate of ?. (Round your answer to three decimal places.) What value for degrees of freedom is associated with this estimate? (b) What percentage of observed variation in hardness can be explained by the linear relationship between hardness and elapsed time? (Round your answer to one decimal place.) _____%A sample consists of 500 houses sold in Karachi between January 2020 and December 2020. The multiple linear regression analysis is carried out to predict the house prices for investment in residential properties in Karachi, Pakistan. The output below is produced using SPSS. Model Unstandardized Coefficients t VIF Constant 14.208 5.736 Age of house -0.299 -2.322 1.58 Square footage of the house 0.364 2.931 1.71 Income of families in the area 0.004 0.392 1.01 Transportation time to major markets -0.337 -2.619 1.90, R2 = 0.67; DW = 2.08 How would you interpret the above ‘Output’ of a regression analysis performed in SPSS?