SCATTER PLOT DATA SETS ANSWER KEY
a)Graph each data set (use graphing calculator) and create a scatter plot – draw a rough sketch of the scatter plot, labeling the axes.
b)Identify the type of correlation you see and write a correlation sentence for the data.
c)Is the correlation the result of causation? If not, tell what the lurking variable might be.
d)Calculate the trend line equation, rounding values to the nearest hundredth.
e)Identify both the slope & y-intercept and interpret their meaning in relationship to the specific data set (sometimes the y-intercept makes no sense)
f)Answer the two questions with each data set using the trend line equation and identify them as using interpolation or extrapolation (rounding to nearest whole number unless indicated otherwise).
1)Height Foot and Length
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b) Positive correlation. Correlation sentence – as height increases, foot length increases.
c) Correlation NOT causation – a person’s height does not determine the foot length – lurking variable “genetics”.
d) TREND LINE EQUATION y = 0.18x – 4.93
e) correlation coefficient – see above value, shows a strong positive correlation
f) slope = 0.18, foot length increases by 0.18 cm for every cm of height increase. Y-intercept = -4.93 cm, foot length when person has no height (!) makes no sense.
g) Interpolation: foot length of person with height 153 cm? (22.8 or 23 cm).
Extrapolation: foot length of person with height 190 cm? (29.5 or 30 cm)
2) Elevation and Temperature
b) Negative Correlation. As the elevation increases, the average temperature decreases.
c) Correlation, NOT causation. The lurking variable would be the thin-ness of the atmosphere.
d) TREND LINE EQUATION y = -3.47x + 69.14
e) correlation coefficient – see above value, shows a somewhatstrong negative correlation
f) slope = -3.47 which means that the average temperature decreases 3.63 degrees Fahrenheit for every thousands feet of elevation gain. Y-intercept = 69.14°F, the average temperature at sea level.
g)Interpolation: what is the average temperature in degrees F. at 6800 feet above sea level? (46°F ).
Extrapolation: what is the average temperature in degrees F at 10,000 feet above sea level?(34°F)
3)Car Mileage and Tread Depth of Tires
b) Negative Correlation. As the distance traveled by your car increases, the tread depth of the tires decreases (they wear out!)
c) Correlation – probably not direct causation. The tread depth would be determined by the amount of wear and tear on the tires which could change depending on types of roads driven on etc. Lurking variables could be quality of tires, road conditions, etc
d) Trend line equation y = -0.14x + 7.17.
e) correlation coefficient – see above value, shows a strong negative correlation
f) Slope is -0.14 which means that every thousand miles your car travels the tread depth decreases by 0.14 cm. Y-intercept is 7.17 cm, the tread depth of a new car.
g) Interpolation – What is the tread depth of a car that has traveled 38,000 miles? (1.9 cm)
Extrapolation – what is the tread depth of a car that has traveled 50,000 miles? (0.2 cm)
4) At the Beach
b) Positive Correlation. As the number of lifeguard rescues increases, the ice cream sales increases.
c) Correlation, not causation – lurking variable – the number of people at the beach. (would cause an increase in both)
d) Trend line equation y = 37.96x + 142.79
e) correlation coefficient – see above value, shows a moderate positive correlation
f) Slope = 37.96 ice cream sales increase by 38 sales for every lifeguard rescue there is. Y-intercept = 142.79 which means when there are no lifeguard rescues there are 143 ice cream sales. (everyone is eating ice cream!)
g) Interpolation – what are the ice cream sales after two lifeguard rescues? (219)
Extrapolation – what are the ice cream sales after 25 lifeguard rescues? (1092)
5) BMX Dirt Bikes – weight of bike VS height of jumps
b)Negative Correlation. As the weight of a dirt bike increases, the height of the jumps it can do decreases.
c)Correlation – possibly causation. Possible lurking variable is the rider’s skill.
d)Trend Line Equation y = -0.16x + 13.35
e) correlation coefficient – see above value, shows a strong negative correlation
f)Slope is -0.16 and it represents the decrease in height in inches for every pound more a dirt bike weighs. (0.16 inches/pound) The y-intercept is 13.35 and represent the height a dirt bike that weighs nothing can jump (! Doesn’t make sense!)
g)Interpolation – What is the jump height of a dirt bike that weighs 23.5 pounds? (9.7 inches)
Extrapolation – what is the jump height of a dirt bike that weighs 26 pounds? (9.3 inches)
6)Light Bulb Life Cost
b) Positive Correlation – the more expensive a light bulb is, the longer life in hours it has.
c) Correlation, probably not causation. Possible lurking variables would be the quality of the materials used to make the lightbulb.
d) Trend line equation y = 406.52x – 181.85
e) correlation coefficient – see above value, shows a strong positive correlation
f) The slope is 406.52 which represents the hours of life per dollar you pay for in a light bulb. The y-intercept is -181.85 hours, which is the life in hours for a free lightbulb (! Doesn’t really make sense, except, “free” doesn’t necessarily mean “good quality”).
g) Interpolation - What is the life in hours of a light bulb that costs $2.50? (834 hours)
Extrapolation – what is the life in hours for a light bulb that costs $4.25? (1546 hours)
7)Survey Results – Movies VS Reading
# of MoviesWatched / 8 / 25 / 5 / 11 / 4 / 25 / 36 / 8 / 38 / 44 / 19 / 8 / 29 / 15 / 31 / 42 / 26 / 7
# of Books Read / 10 / 15 / 3 / 7 / 2 / 6 / 8 / 25 / 14 / 5 / 22 / 6 / 26 / 19 / 21 / 13 / 2 / 8
No correlation – There is no correlation between the number of movies a person watches and the number of books they read.
Cannot calculate a trend line equation, cannot make any predictions using either interpolation or extrapolation.