Exam 6: Scatterplots, association, and Correlation

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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.Describe the association shown in the scatterplot. 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.Describe the association shown in the scatterplot.

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Year,results of race

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The paired data below consist of the height (in cm)of children and their reading scores.If the height was recorded in inches,what would be the correlation? Height () Reading Scores 117.5 66 128.9 71 122.6 68 131.45 75 132.7 76 136.5 79 120 68 139.1 80

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A reporter investigates speeding on roads in a county and finds a correlation of 0.961 between the number of speeding tickets and the numbers of kilometres of well-paved roads.Assuming that the relation is linear,does it mean that there are more speeding tickets on well-paved roads?

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The owner of a small manufacturing plant employs nine people.As part of their personnel file,he asked each one to record the distance,in km,they travel one way from home to work and the time it takes in minutes. Time () Distance () 5.2 18 2.3 8 4.1 10 6.4 19 3.8 8 1.8 6 7.1 26 9.5 32 1.8 8

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Owners of a new appliances store tracked sales (in thousands)for the first 10 days,and displayed the data in a scatterplot.Make a histogram of the daily sales since the shop has been in business. Owners of a new appliances store tracked sales (in thousands)for the first 10 days,and displayed the data in a scatterplot.Make a histogram of the daily sales since the shop has been in business.    Owners of a new appliances store tracked sales (in thousands)for the first 10 days,and displayed the data in a scatterplot.Make a histogram of the daily sales since the shop has been in business.

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A reporter studied the causes of a fire to a house,and established thanks to a scatterplot a strong correlation between the damages (in dollars)and the number of firefighters at the scene.Find the lurking variable,if there is one.

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The following table gives the total sales (revenue)and profits for 8 retailers.  Company  Total Sales  (Millions of $)  Profits  (Millions of $)  Adams 45.02.6 Brown 15.00.8 Clay 57.02.2 Donner 9.50.5 Esters 22.01.4 Framer 35.01.8 Gillies 64.03.0 Hays 27.50.9\begin{array} { l c c } \hline \text { Company } & \begin{array} { c } \text { Total Sales } \\\text { (Millions of \$) }\end{array} & \begin{array} { c } \text { Profits } \\\text { (Millions of \$) }\end{array} \\\hline \text { Adams } & 45.0 & 2.6 \\\text { Brown } & 15.0 & 0.8 \\\text { Clay } & 57.0 & 2.2 \\\text { Donner } & 9.5 & 0.5 \\\text { Esters } & 22.0 & 1.4 \\\text { Framer } & 35.0 & 1.8 \\\text { Gillies } & 64.0 & 3.0 \\\text { Hays } & 27.5 & 0.9 \\\hline\end{array}  The following table gives the total sales (revenue)and profits for 8 retailers.  \begin{array} { l c c }  \hline \text { Company } & \begin{array} { c }  \text { Total Sales } \\ \text { (Millions of \$) } \end{array} & \begin{array} { c }  \text { Profits } \\ \text { (Millions of \$) } \end{array} \\ \hline \text { Adams } & 45.0 & 2.6 \\ \text { Brown } & 15.0 & 0.8 \\ \text { Clay } & 57.0 & 2.2 \\ \text { Donner } & 9.5 & 0.5 \\ \text { Esters } & 22.0 & 1.4 \\ \text { Framer } & 35.0 & 1.8 \\ \text { Gillies } & 64.0 & 3.0 \\ \text { Hays } & 27.5 & 0.9 \\ \hline \end{array}

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A ceramics factory can fire six large batches of pottery per day.Sometimes in the process a few of the pieces break.In order to understand the problem better,the factory records the number of broken pieces in each batch for 4 days and then creates the scatterplot shown.Make a histogram showing the distribution of the number of broken pieces in the 24 batches of pottery examined. A ceramics factory can fire six large batches of pottery per day.Sometimes in the process a few of the pieces break.In order to understand the problem better,the factory records the number of broken pieces in each batch for 4 days and then creates the scatterplot shown.Make a histogram showing the distribution of the number of broken pieces in the 24 batches of pottery examined.

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The relationship between two quantities X and Y is examined,and the association is shown in the scatterplot below. The relationship between two quantities X and Y is examined,and the association is shown in the scatterplot below.   What re-expression of Y should be tried as a starting point? What re-expression of Y should be tried as a starting point?

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One of the important factors determining a car's fuel efficiency is its weight.This relationship is examined for 11 cars,and the association is shown in the scatterplot below. One of the important factors determining a car's fuel efficiency is its weight.This relationship is examined for 11 cars,and the association is shown in the scatterplot below.   Describe the association between these variables shown in the scatterplot. Describe the association between these variables shown in the scatterplot.

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Student: grade point average,student: height (feet)

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A study is conducted on insects growth based on hydrometry.The correlation found between insects growth and hydrometry is 0.05.A journalist concludes that a low correlation between insects growth and hydrometry shows that insects can reproduce easily in a dry climate.Do you agree with this interpretation?

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Two different tests are designed to measure employee productivity and dexterity.Several employees are randomly selected and tested with these results. Productivity Dexterity 23 49 25 53 28 59 21 42 21 47 25 53 26 55 30 63 34 67 36 75

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Oranges: circumference (centimetres),oranges: weight (grams)

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Below are the Olympic gold medal performances in the men's high jump from 1960 to 1984. Year High Jump (in.) 1960 85.25 1964 85.75 1968 88.25 1972 87.75 1976 88.50 1980 92.50 1984 92.50 1988 93.75 1992 92.25 1996 94.00 2000 92.50 2004 93.00 2008 93.00 2012 93.75  Below are the Olympic gold medal performances in the men's high jump from 1960 to 1984.  \begin{array} { l l }  \hline \text { Year } & \text { High Jump (in.) } \\ \hline 1960 & 85.25 \\ \hline 1964 & 85.75 \\ \hline 1968 & 88.25 \\ \hline 1972 & 87.75 \\ \hline 1976 & 88.50 \\ \hline 1980 & 92.50 \\ \hline 1984 & 92.50 \\ \hline 1988 & 93.75 \\ \hline 1992 & 92.25 \\ \hline 1996 & 94.00 \\ \hline 2000 & 92.50 \\ \hline 2004 & 93.00 \\ \hline 2008 & 93.00 \\ \hline 2012 & 93.75 \\ \hline \end{array}

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To get the best deal on a microwave oven,Amanda called six appliance stores and asked the cost and volume of several models.The prices and volumes she was quoted are listed below. Volume ( cu.ft) Price (\ ) 1.9 183 0.5 119 2.2 119 1.8 417 1.5 463 1 200 1.5 279 0.7 49 1.5 349

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