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Physics 270

Physics 270. y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

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Page 1: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

Physics 270

Page 2: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

y(x) Data Set #1

t (s) y (cm)

1 1.3

2 3.5

3 4.2

4 5.0

5 7.0

6 8.8

7 10.1

8 12.5

9 13.0

10 15.6

Page 3: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 4: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

What about error bars?

Page 5: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

Data Set #2

t (s) y (cm)

1 0.8

2 3.0

3 3.5

4 4.2

5 5.1

6 5.9

7 6.8

8 7.5

9 8.1

10 9.0

Page 6: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 7: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

Simple linear regression describes the linear relationship between a predictor variable, plotted on the x-axis, and a response variable, plotted on the y-axis

Independent Variable (X)

depe

nden

t V

aria

ble

(Y)

Page 8: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

1oy a a x

X

Y

oa

1.0

1a

Page 9: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 10: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

The best linear approximation involves finding values of a0 and a1 to minimize

Page 11: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 12: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 13: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 14: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 15: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 16: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

Am. J. Phys. 67, 528 (June 1999).Barbara S. Andereck

Page 17: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 18: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 19: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 20: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 21: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6
Page 22: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

Carefully read all of chapter 6 in the text.

Then, do problems 6.4 and 6.5.Hand in the written out equations that

you use, showing all work, your results, and the computer program, Mathematica, or Excel worksheet used.

Page 23: Physics 270.  y ( x )Data Set #1 t (s) y (cm) 11.3 23.5 34.2 45.0 57.0 68.8 710.1 812.5 913.0 1015.6

Test covers chapters…1, 2, 3, and 6 of the textbook.

You may prepare both sides of an 8 ½ by 11 inch sheet with equations, examples, notes, or anything else you may wish to have with you. You will need your calculator.