Exam 9: Re-Expressing Data: Get It Straight

A rock is dropped from a tall building and its distance (in feet)below the point of release is recorded as accurately as possible at various times after the moment of release.The results are shown in the table.Use technology to create a curved model for the data.

It's easy to measure the circumference of a tree's trunk,but not so easy to measure its height.Foresters developed a model for ponderosa pine trees that they use to predict the tree's height (h,in metres)from the circumference of its trunk (c,in centimetres): ln = -1.2 + 1.4(ln c).A lumberjack finds a tree with a circumference of 30 cm.How tall does this model estimate the tree to be?

The relationship between two quantities x and y is examined,and the association is shown in the scatterplot below. Describe the association between these variables shown in the scatterplot.

The relationship between two quantities x and y is examined.The relationship appears to be fairly linear.A linear model is considered,and the regression analysis is as follows: Dependent variable: y R-squared = 87.9% VARIABLE COEFFICIENT Intercept 37.74 X -9.97 What does the slope say about the relationship between x and y?

For the model = 2.93( ),predict y when x = 2.Round to two decimal places.

A forester would like to know how big a maple tree might be at age 50 years.She gathers data from some trees that have been cut down,and plots the diameters (in inches)of the trees against their ages (in years).First she makes a linear model.The scatterplot and residuals plot are shown.If she uses this model to try to predict the diameter of a 50-year old maple tree,would you expect that estimate to be fairly accurate,too low,or too high? Explain.

Doctors studying how the human body assimilates medication inject a patient with penicillin,and then monitor the concentration of the drug in the patient's blood for several hours.The data are shown in the table. Straighten the scatterplot by re-expressing these data and create an appropriate model for predicting the concentration of penicillin.

A psychology graduate student is studying the effect of alcohol intoxication on a person's ability to perform manual tasks.In a very simple experiment,a subject's blood alcohol level is brought to a certain level and then the subject is presented with 10 rope knots.The subject then attempts to untie as many knots as he or she can in 30 seconds.The results of the experiments are summarized in the table below. a)Re-express the number of knots untied by taking the inverse of each count,then plot the re-expressed data as a scatterplot. b)Determine the regression equation and correlation coefficient for the re-expressed data. c)Interpret the y-intercept of your model.Does it have meaning?

The model = 12 + 20(dia)can be used to predict the breaking strength of a rope (in kilograms)from its diameter (in metres).According to this model,how much force should a rope one-half metre in diameter be able to withstand?

QuarkNet,a project funded by the National Science Foundation and the U.S.Department of Energy,poses the following problem on its website: "Last year,deep within the Soudan mine,QuarkNet teachers began a long-term experiment to measure the amount of carbon-14 remaining in an initial 100-gram sample at 2000-year intervals.The experiment will be complete in the year 32001.Fortunately,a method for sending information backwards in time will be discovered in the year 29998,so,although the experiment is far from over,the results are in." Here is a portion of the data: A scatterplot of these data looks like: Can you use your model to predict when 50 g of the sample will be left? Explain.

Dioxins are a class of long-lived and highly toxic pollutants.The topsoil concentration in parts per million (ppm)are shown in the table below as a function of distance from the dump. Create an appropriate model to re-express the Concentration (ppm).Then use your model to predict the dioxin concentration at a distance of 400 metres.Round all figures to 4 decimal places.