T-Distance(mT-Distance Un c.un) Time(s) -TimeUnc. (s) i speedert st 9.0430 Trial

Question

T-Distance(mT-Distance Un c.un) Time(s) -TimeUnc. (s) i speedert st 9.0430 Trial # t o.s 2-35 s 2.925 2.92 3-40s 0 3.3 0.S 5. Average speed Standard deviation Uncertainty of the average Y-Intercept Standard Deviation of the slope Questions 1) What is the difference between percent error and percent difference? Explain. 2) If your work bench was sloped, what type of error would this produce? 3) If a cluster of data has a low standard deviation, what does that tell us about the spread? 4) What is the difference between RMSE, linear regression, and "best-fit"? Include the answer to these questions in your lab report.

Explanation / Answer

1.average speed is  x=c(8.04,17.5,11.3,14.8,13.6,19.0,20.0,16.4)

mean(x)=15.08

2. sd of average speed

errors y=c(3.07,.80,1.85,1.50,1.38,1.11,.72,1.08)

let z=x+y

w=x-y

z,w are the data points of average speed

standard deviation of avaerage speed

v=c(11.11 18.30 13.15 16.30 14.98 20.11 20.72 17.48 4.97 16.70 9.45 13.30
12.22 17.89 19.28 15.32)

is 4.2245

3.uncertainity of average =( x(max)-x(min))/2sqrt(n)=2.114

4.Y intercept = mean+_ (max(d)-min(d))/2= 55.6+-39.1

5.here d is distance and t is in time

> d=c(d+.5,d-.5)
> d
[1] 19.4 84.3 33.6 43.8 46.9 61.7 97.6 61.5 18.4 83.3 32.6 42.8 45.9 60.7 96.6
[16] 60.5
> t=rep(c(2.35,4.78,2.92,2.92,3.40,3.23,4.85,3.73),2)
> t
[1] 2.35 4.78 2.92 2.92 3.40 3.23 4.85 3.73 2.35 4.78 2.92 2.92 3.40 3.23 4.85
[16] 3.73
> d/t
[1] 8.255319 17.635983 11.506849 15.000000 13.794118 19.102167 20.123711
[8] 16.487936 7.829787 17.426778 11.164384 14.657534 13.500000 18.792570
[15] 19.917526 16.219839
> sd(d/t)
[1] 3.878991
so the sd for slope is 3.8789

QUESTIONS

PERCENT ERROR

When comparing an experimental result to a value determined by theory or to an accepted known value (like

g = 9.8 m/s2)

we determine the difference between the experimental value and the theoretical value as a percentage of the theoretical value. In the definition below, "theoretical" is the value that is determined from theory (i.e., calculated from physics equations) or taken as a known or accepted value like g.

( 1 )

% error =

PERCENT DIFFERENCE

When wanting to compare two values that are both determined by experimentation, we don't have a "correct" or accepted value to which to compare, so we simply look at how different the two values are as a percentage of their average value:

( 2 )

% difference =

*100%

2.

sorry i didnt get this

3.

. The more spread out a data distribution is, the greater its standard deviation.

4.The RMSE is the square root of the variance of the residuals. It indicates the absolute fit of the model to the data–how close the observed data points are to the model’s predicted values

linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables)

A line of best fit (or "trend" line) is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points.

|theoretical experimental|/theoritical *100 %

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