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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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