In addition to quadratic and exponential models, another common type of model is called a power model. Power models are models in the form hat{y}=a cdot x^{p}. Here are data on

a2linetagadaW 2021-01-06 Answered

In addition to quadratic and exponential models, another common type of model is called a power model. Power models are models in the form y^=a  xp. Here are data on the eight planets of our solar system. Distance from the sun is measured in astronomical units (AU), the average distance Earth is from the sun. PlanetDistance from sun(astronomical units)Period of revolution(Earth years)Mercury0.3870.241 Venus 0.7230.615 Earth 1.0001.000 Mars 1.5241.881 Jupiter 5.20311.862 Saturn 9.53929.456 Uranus 19.19184.070 Neptune 30.061164.810 Calculate and interpret the residual for Neptune.

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BleabyinfibiaG
Answered 2021-01-07 Author has 118 answers
Step 1Note: The solution gives the commands for the calculation using aTi83/84-calculator. If you use a different type of technology, then the commands will differ.Press on STAT and then select 1:Edit ... Enter the data of distance from the sun in the list L1 and enter the data of period of revolution in the list L2.Next, press on STAT, select CALC and then select PWT Reg. Next, we need to finish the command by entering L1, L2.
PWT Reg L1, L2Finally, pressing on ENTER then gives us the following result:y=a  xb
a=1.003
b=1.4998
r2=1This then implies that the regression line is:y^=a  xb=1.0003  x1.4998where x represents the distance from sun and y represents the period of revolution.Step 2Given:x=30.061
y=164.810Evaluate the equation of the regression line at x=30.061:
y^=1.0003  30.0611.4998  164.7631The residual is the difference between the observed y-value and the predicted y-value.Residual =y  y^ =164.810  164.7631=0.0469Neptune's period of revolution is 0.0469 earth years longer than expected.
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