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The number of daylight hours H at noon in City X was measured on the 21st of each month for eight consecutive months (m=1 for January, …, m=8 for August). The results are shown below; the value for May (m=5) was lost in transcription.
Assuming the data follows a linear model over this period, find the regression line of H on m for the seven known points.
Use your line to estimate the daylight hours on the 21st of May (m=5).
Explain why your line should not be used to estimate the month m at which H=17.0h.
Explain in context why your line should not be used to predict the daylight hours on the 21st of December (m=12).
State a more appropriate model for H over an entire year. You are not expected to calculate any parameters.
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Denise brews a cup of coffee and leaves it in a room at a constant 20°C. She uses a temperature probe to record the coffee’s temperature every 4 minutes, obtaining the following data:
After graphing the data, Denise believes a suitable model will be T=20+abt,a,b∈R.
Explain why T−20 can be modeled by an exponential function.
Find the equation of the least squares exponential regression curve for T−20.
Write down the coefficient of determination, R2.
Interpret what the value of R2 implies about the model.
Hence predict the temperature of the coffee after 14 minutes.
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An astronaut measures the height above the moon's surface, h meters, of a rock t seconds after releasing it. The following table shows the recorded values of h and t2.
State the height from which the rock was released.
The relationship between h and t2 can be modeled by the equation h=at2+b.
Find the value of a and the value of b.
Hence estimate the time at which the rock reaches a height of 20 meters.
Explain why the regression equation should not be used to predict the height when t=9.
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