Presentation on theme: "AP Statistics: Section 4.1 C Power Law Models. Power growth can be modeled by the equation _______, where a and b are constants. (Notice that in exponential."— Presentation transcript:
AP Statistics: Section 4.1 C Power Law Models
Power growth can be modeled by the equation _______, where a and b are constants. (Notice that in exponential growth, x is the _________, while in power growth, x is the _____.) exponent base
We can model power growth using a LSL as follows: Take the ln of both sides. The ln of a product equals the sum of the ln’s. The ln of a power equals the power times the ln.
Notice that there is a linear relationship between ln y and ln x and that b is the slope of the straight line that links ln y to ln x.
On July 31, 2005, a team of astronomers announced they had discovered what seemed to be a new planet in our solar system. Xena, the potential planet, is bigger than Pluto and has an average distance from the sun of 9.5 billion miles ( astronomical units). Could Xena be a new planet?
Graph the scatterplot of the planetary data. Describe it. Positive Curved Strong
Graph distance vs. ln (period). Describe it. Positive Curved Strong
Graph ln (distance) vs. ln (period). Describe it. Positive Linear Strong
r 2 = ________ and the LSL is ____________________________
Plot the residuals. Discuss. There is a curved pattern, BUT the residuals are really quite small so we will live with it.
Find the prediction equation and predict the period for Xena.