A physics student wants to measure the stiffness of a spring (force required per cm stretched). He knows that according to Hooke's law, there is a linear relationship between the distance a spring is stretched and the force needed to stretch the spring. He collects some data by measuring the force applied to the spring when he stretches the spring by some amount. The plot and the least squares fit is given below. From the regression model, the intercept was found to be -2.532 and the slope was found to be 25.321. Part i). The stiffness of the spring was predicted to be A. -9.961 B. 25.321 C. 50.642 D. -2.532 E. 125.84 Part ii). Refer to the previous question, the physics student used the regression model to predict that a force of 377.28N would be required to stretch the spring by 15cm. Remarkably, his prediction was horribly wrong. Can you explain why? (Check all that apply) A. He made a prediction outside of the range of forces observed. B. He had outliers or influential points in his data. C. Correlation does not imply causation. D. He made a prediction outside of the range of stretched distances measured. E. None of the above
A physics student wants to measure the stiffness of a spring (force required per cm stretched). He knows that according to Hooke's law, there is a linear relationship between the distance a spring is stretched and the force needed to stretch the spring. He collects some data by measuring the force applied to the spring when he stretches the spring by some amount. The plot and the least squares fit is given below.
From the regression model, the intercept was found to be -2.532 and the slope was found to be 25.321.
Part i).
The stiffness of the spring was predicted to be
A. -9.961
B. 25.321
C. 50.642
D. -2.532
E. 125.84
Part ii).
Refer to the previous question, the physics student used the regression model to predict that a force of 377.28N would be required to stretch the spring by 15cm. Remarkably, his prediction was horribly wrong. Can you explain why? (Check all that apply)
A. He made a prediction outside of the
B. He had outliers or influential points in his data.
C.
D. He made a prediction outside of the range of stretched distances measured.
E. None of the above
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