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Data Gathering and Analysis Assignment.

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Any measuring device that makes an indirect measurement to come up with a supposedly accurate answer relies on calibration for accuracy. For example, an electronic laboratory balance measures changes in electrical resistance in “load cells” and is calibrated to correlate particular resistance measurements with the weight that caused the changes. Your task is to select or create an appropriate measurement device and produce a formula that will enable that device to make accurate (or more accurate) measurements. Make a series of measurements (preferably at least 20 if possible) ag...

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Question Preview:

Any measuring device that makes an indirect measurement to come up with a supposedly accurate answer relies on calibration for accuracy. For example, an electronic laboratory balance measures changes in electrical resistance in “load cells” and is calibrated to correlate particular resistance measurements with the weight that caused the changes. Your task is to select or create an appropriate measurement device and produce a formula that will enable that device to make accurate (or more accurate) measurements. Make a series of measurements (preferably at least 20 if possible) against accurately known standards. You can either use the raw data (like the balance resistance measurements, if you can get at them) or the measurement the device produces (like the weight shown on the balance display). If you use the measurements the device produces, it would be best if you use a device that you suspect is not giving very accurate measurements, and your formula will enable you to improve its accuracy. Graph the measurements against the standards and determine a formula that would best enable you to make accurate measurements or correct the answers the device gives. Log transform the data if necessary. Produce a graph showing the Olympic Games gold medal times for the men’s 100 metre sprint event from as far back as you can find to 2012. Use the Excel Chart Labeler Add-In to enter the names of the athletes on the graph.

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Solution Preview

I have used a weight scale to measure the weight of Dumbbell whose actual weight I know already. I have measured the weight of 20 Dumbbell using this weight scale and the results are as shown below from where we observe that weight scale is not much accurate in measuring the actual weight.

We created the scatter plot of the Dumbbell actual weight as dependent and  Dumbbell weight measured using weight scale as independent variable as follows from where we observe that there is almost a good straight line relationship between the two variables and hence we have no need to use any transformation of data.

Formula in appropriate word is the estimated regression line as follows:

Actual weight of Dumbbell (Kg)

= 0.563  +  0.981 Weight of Dumbbell  measured using new Scale

For within range data let us take Weight of Dumbbell  measured using new Scale as 5.2Kg whose actual weight is 6 kg then estimated actual weight of Dumbbell is

Estimated Actual weight of Dumbbell (Kg)

=0.563  +  0.981*5.2

 =5.6642 Kg which  is close to actual Dumbbell weight of 6kg.

For outside of range let us take Weight of Dumbbell  measured using new Scale as 30 Kg the estimated actual weight is

Estimated Actual weight of Dumbbell (Kg) =0.563  +  0.981*30  =29.993 Kg.

The estimated regression line to predict time from year from scatter plot is as follows:

Time = 36.41 – 0.013 Year of Games

Hence in year 2016  Time= 36.41 – 0.013 *2016  =10.202 seconds

Also, in year 2020 Time= 36.41 – 0.013 *2020  =10.15 seconds

 The resulting times are not close to 9.65 seconds and hence prediction are not good by the regression line estimated.

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