NCSSM HONORS/AP STATISTICS

Worksheet #1: Interpreting Slope and y-Intercept

For each problem below, provide a written interpretation of both the slope and the y-intercept. Be sure to include correct units of measure in your responses. Example: Scientists rated the activity level of fish at different temperatures and are trying to determine if the water temperature affects the fish’s activity. They calculated a linear regression equation of y = 148.6 – 3.2x where x = the temperature of the water (in °C) and y = the measure of fish activity. Solution: Slope = -3.2 … The fish activity decreases 3.2 for every 1°C increase in temperature. y-Intercept = 148.6 … When the water is 0°C, the fish activity would be 148.6. 1) Fishermen in the Fingers Lakes region of the US have been recording the dead fish they encounter

while fishing in the region. The Department of Environmental Conservation monitors the pollution index for the Finger Lakes region. The model for the number of fish deaths for a given pollution index is y = 111.958 + 9.607x where x = the pollution index and y = the number of fish deaths.

2) A statistician decides to test the accuracy of the statement “You will never have as many friends in

your life as you do in high school”. She finds a linear regression equation to model the data she gathered: y = 116.14 – 2.94x where x = age of person and y = number of friends the person has.

3) A student with no previous typing experience takes a 3-week typing course and after each day takes a

test. The speed is recorded in words per minute (wpm). A linear regression equation that models the student’s results is found to be y = 23.5 + 2.0x where x = the number of days after the student started the course and y = the student’s recorded typing speed.

4) The busiest season for Walmart is the Christmas holiday and weekends see a tremendous number of

customers. Last year, Walmart conducted a study as to the amount of waiting time in checkout lanes its customers had to wait. Based on the collected data, the linear regression model is found to be y = 9.9 – 0.445x where x = the number of lanes open and y = the wait time (in minutes).

5) A diver is investigating a wreck under water and has to come up to the surface slowly. A linear

regression model of y = 225.7 – 17.1x is found where x = the time from which the diver starts ascending (in minutes) and y = the depth (in feet).

Should you need a review of how to properly interpret a line’s slope and y-intercept, here are a couple of websites that should be of help.

§ The Meaning of Slope and y-Intercept in Word Problems ... http://www.purplemath.com/modules/slopyint.htm

§ Understanding the Regression Line … http://www.ltcconline.net/greenl/courses/201/Regression/CorrelationHandout.htm