Marbles were rolled down a ramp and their speed at the bottom of the ramp
was measured to determine if the mass affects the speed of the marble.
The theory predicts that the speed is independent of the mass.
The theory says the mass of the marble does not affect the speed.
_________ Calculate the sample size n.
_________ Calculate the slope of the linear regression.
_________ Calculate the y-intercept of the linear regression.
_________ Is the relation between mass (g) and speed (cm/s) positive, negative, or neutral?
_________ Calculate the correlation coefficient r for the data.
______________ Is the correlation none, weak/low, moderate, strong/high, or perfect?
______________ Determine the coefficient of determination.
______________ What percent in the variation in mass (g) "explains" the variation in speed (cm/s)?
_________ Use the slope and intercept to predict the speed (cm/s) for a mass (g) equal to 6 g.
_________ Use the slope and intercept to determine the mass (g) at which the speed (cm/s) is predicted to be 30 cm/s.
Does the data support the theory of no relationship between mass and speed?
Why or why not? Helpful suggestion for answering this: What does the correlation tell you about the relationship?
1 sample size n 8
2 slope -1.11
3 intercept 34.06
4 nature negative or neutral/random
5 correlation -0.23
6 strength weak
7 coef det 0.053
8 perc variation 5.30%
9 6 g. 27.41 speed (cm/s)
10 30 cm/s 3.66 mass (g)
11 inference yes
12 inference the correlation is weak at best, the sample size is small
the theory says NO relation, a weak correlation does not
prove a relationship exists. The correlation can be
artificially high for small samples: two points make
a perfect correlation, a single line, and prove nothing.
ttest: -0.5796
p-value: 0.5832682
max c 0.4167318
Questions phrased in the negative are harder to answer.