Regression Word Problems

The data table in the picture shows the average length of daylight for each month of the year.  Calculate the sinusoidal regression equation of the data.

• y = 2.69sin(0.512x - 1.47) + 11.89
• y = 11.89sin(2.69x + 0.512) - 1.47
• y = -0.106x + 12.44
• y = 12.44x - 0.106

This equation models the data from question 1, where x stands for month of the year and y stands for daylight hours.  Use the equation to predict th length of daylight during the month of May.

• 5 hours
• 14.28 hours
• 11.9 hours
• 13.85 hours

Calculate the period of the regression equation.

• 12.27
• 0.512
• 2.69
• 2.34

What would be the ideal (expected) period for this data?

• 12 since there are 12 months in the year.
• 365 since there are 365 days in the year.
• 24 since there are 24 hours in a day.
• 5 since May is the 5th month.

What is the range of daylight hours according to this regression equation?

• 9.2 to 14.6
• 8.8 to 15.2
• 9.8 to 13.2
• 11.3 to 12.4

At a pier, scientists measure the depth of the water according to the tides.  At high tide, the water depth is 8 feet.  At low tide, 6.2 hours later, the depth is 5 feet.  Which of the following shows how you would fill-in the next 4 depths in the table?

• 6.5,  5,  6.5,  8
• 4,  0,  4,  8
• 5,  2.5,  5,  8
• 5,  8,  5,  8

At a pier, scientists measure the depth of the water according to the tides.  At high tide, the water depth is 8 feet.  At low tide, 6.2 hours later, the depth is 5 feet.  Calculate the sinusoidal regression equation that models this scenario.

• 1.5sin(0.507x + 1.57) + 6.5
• 0.507 sin(1.5x + 6.5) + 1.57
• y = 6.8x
• y = 6.2x + 5

At a pier, scientists measure the depth of the water according to the tides.  At high tide, the water depth is 8 feet.  At low tide, 6.2 hours later, the depth is 5 feet.  Use the equation to predict the depth after 4 hours.

• 4 feet deep
• 5.84 feet deep
• 5.42 feet deep
• 4.98 feet deep.

At a pier, scientists measure the depth of the water according to the tides.  At high tide, the water depth is 8 feet.  At low tide, 6.2 hours later, the depth is 5 feet.  Use the equation to calculate how many hours it will be before the water depth is first below 7 feet?

• 9.96 hours
• 2.43 hours
• 2.91 hours
• 1.89 hours

At a pier, scientists measure the depth of the water according to the tides.  At high tide, the water depth is 8 feet.  At low tide, 6.2 hours later, the depth is 5 feet.  Use the equation or table to decide: how often does the tide cycle repeat?

• Once every 3.1 hours.
• Once every 6.2 hours.
• Once every 9.3 hours.
• Once every 12.4 hours.