AP Stats Inference for Slopes

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. The equation of the least-squares regression line for predicting selling price from appraised value is

To determine property taxes, Florida reappraises real estate every year, and the county appraiser's website lists the current "fair market value" of each piece of property. Property usually sells for somewhat more than the appraised market value. We collected data on the appraised market values x and the actual selling prices y (in thousands of dollars) of a random sample of 16 condominium units in Florida. We checked that the conditions for inference about the slope of the population regression line are met. Here is part of the Minitab output from a least-squares regression analysis using these data. The slope beta of the population regression line describes

• the exact increase in the selling price of an individual unit when its appraised value increases by $1000.

• the average increase in the appraised value in a population of units when selling prices increases by $1000.

• the average increase in selling prices in a population of units when appraised value increases by $1000.

• the average increase in the appraised value in the sample of units when selling price increases by $1000.

• the average increase in selling price in the sample of units when the appraised value increases by $1000.

The computer output below shows the result of a linear regression analysis for predicting the concentration of zinc, in parts per million (ppm), from the concentration of lead, in ppm, found in fish from a certain river. Which of the following statements is a correct interpretation of the value 19.0 in the output?

• On average there is a predicted increase of 19.0 ppm in concentration of lead for every increase of 1 ppm in concentration of zinc found in the fish.

• On average there is a predicted increase of 19.0 ppm in concentration of zinc for every increase of 1 ppm in concentration of lead found in the fish.

• The predicted concentration of zinc is 19.0 ppm in fish with no concentration of lead.

• The predicted concentration of lead is 19.0 ppm in fish with no concentration of zinc.

• Approximately 19% of the variability in the zinc concentration is predicted by its linear relationship with lead concentration.

The computer output is used to predict helicopter flight time from drop height.  Which is the correct equation for this relationship?

• (Time) = -0.03761+0.0057244(drop height)

• (time) = -0.03761+0.05838(drop height)

• (height)=-0.03761+0.0057244(time)

• (height)=0.0057244-0.03761(time)

Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears. Here is some computer output from a linear regression analysis of these data. Which of the following represents a 95% confidence interval for the slope of the population least-squares regression line relating the weight of a bear and its neck girth, assuming the conditions for inference are met?

• A

• B

• C

• D

• E

Raoul performed an experiment using 16 windup rubber band single-propeller airplanes. He would up the propeller a different number of times and recorded the amount of time (in seconds) that the airplane flew for each number of rotations that the propeller was wound. Which of the following is a 95 percent confidence interval for the slope of the regression line that relates the number of rotations to the plane's flight time?

• 0.0462 ± (2.145)(0.01565)

• 0.924 ± (2.145)(0.6413)

• 0.0462 ± (2.96)(0.01565)

• 0.924 ± (2.96)(0.6413)

• 0.0462 ± (2.131)(0.01565)

Park rangers are interested in estimating the weight of the bears that inhabit their state. The rangers have data on weight (in pounds) and neck girth (distance around the neck in inches) for 10 randomly selected bears. Here is some computer output from a linear regression analysis of these data. Which of the following represents a 95% confidence interval for the slope of the population least-squares regression line relating the weight of a bear and its neck girth, assuming the conditions for inference are met?

If the line of best fit shows the relationship between elevation and average annual temperature in celsius, what does the slope represent? Assume the line of best fit is represented by the equation \(y=-\frac{1}{160}x+22.5\)

• For every 160 meters in elevation there's a decrease of 1 Celsius in temperature

• For every meter of elevation there's a decrease of 1 Celsius in temperature 

• For every  160 meters in elevation there's an increase of 1 Celsius in temperature

• For every 22.5 meters there's a decrease of 1/160 Celsius in temperature.

• A plane ride costs $0.136 (13 cents)

• For every 1 mile flown, the cost goes up  $ 0.136 dollars (13 cents)

• For every 1 mile flown, the cost goes up $74