4. The following set of data were taken for the displacement x of a cart on an a

Question

4. The following set of data were taken for the displacement x of a cart on an air track as a function of time t. Calculate t2 for each of the data points form a linear least squares fit to x abscissa. Record the slope and correlation coefficient below. and then per- versus t2, where x is the ordinate and t2 is the 0.6000 10.250 2190 1.lb16:051 9150 15-oa Correlation Coefficient-D 99429 x (m) 0.1500.338 0.975 1.48 1.37 3.03 0.930 2.45 t (s) 2.04 2.46 3.95 (2 Slope·Derso mo. Laboratory 45 7. Find the angle of inclination of the air track in question 4, which gives the accel- eration that you found in question 5.

Explanation / Answer

Regression Analysis: x versus t^2

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.0313952 99.89% 99.86% 99.56%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -0.0154 0.0174 -0.89 0.417
t^2 0.15590 0.00234 66.56 0.000 1.00

Regression Equation

x = -0.0154 + 0.15590 t^2

slope = 0.1559

correlation coefficient = sqrt(R^2)

= sqrt(0.9989)

correlation coefficient = 0.9994

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