The speed of a marble rolling into a line of marbles was recorded by the SC 130 Physical Science students. When the inbound marble struck a line of five stationary marbles, one marble was ejected from the stationary line of marbles. The speed of the ejected marble was recorded as the speed out.
_________ Calculate the sample size n.
_________ Calculate the slope of the linear regression.
_________ Calculate the y-intercept of the linear regression.
_________ Is the relation between speed in and speed out 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 speed in "explains" the variation in speed out?
_________ Use the slope and intercept to predict the speed out at which the speed in equals 10 cm/s.
_________ Use the slope and intercept to determine the speed in at which the speed out is predicted to be 20 cm/s.
1sample size n 8
2slope 0.36
3intercept -1.56
4nature positive
5correlation 0.82
6strength strong
7coef det 0.667
8perc variation66.74%
910cm/s2.05 speed Out (cm/s)
1020 cm/s59.78 speed In (cm/s)
11inferenceyes
12inferencethe 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: 3.4695
p-value: 0.0133116
max c 0.9866884