MATH 225N Week 8 Interpret the Slope & Y-Intercept of the Least Squares Regression Line
Question
A scientific study on gerbil population growth results i
... [Show More] n the data below.
x y
8 63
11 77
14 86
17 90
20 140
The least squares regression line modeling this data is given by yˆ=13.3+5.567x. What is the intercept of the regression line? Round your answer to one decimal place.
Answer 1:
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Keep trying - mistakes can help us grow.
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$$3
Answer 2:
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Not quite - review the answer explanation to help get the next one.
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$$17
Answer Explanation
Correct answers:
• $13.3$13.3
The equation y=mx+b defines a line with a slope of m and a y-intercept of b. In this case the intercept or the constant added to x is 13.3.
Question
True or False: The more mangoes you eat, the more rashes you get.
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Well done! You got it right.
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True
False
Answer Explanation
Correct answer:
False
Many things can cause an increase or decrease in rashes: diet, exercise, hormones, medication, etc. There are too many other confounding variables that it can not be determined that Mango's are the cause of a rash.
Understand the difference between correlation and causation
Question
Suppose that a large controlled experiment tests whether caffeine improves reaction times. A very large number of randomly selected participants are randomly given identical-seeming pills with varying doses of caffeine (including none) and then given tests of reaction times under the same conditions. The experiment finds a strong negative correlation between caffeine dose and reaction time. (Note that lower reaction times are better.)
Identify what can be concluded based on this information.
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Not quite right - check out the answer explanation.
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There is evidence that caffeine causes lower (better) reaction times.
People with lower (better) reaction times generally choose to consume more caffeine.
Lower reaction times are associated with higher caffeine doses, but this study provides no evidence that caffeine causes lower reaction times.
There is no relationship between reaction time and caffeine.
Answer Explanation
Correct answer:
There is evidence that caffeine causes lower (better) reaction times.
Correlation alone does not prove causation, but this scenario provides more evidence than just correlation between two variables. Since the data were obtained from an appropriately randomized controlled experiment, a correlation can be used as evidence of a causal relationship. Since all other variables were controlled, there is no third variable that could be associated with caffeine that actually causes differences in reaction times.
Your answer:
Lower reaction times are associated with higher caffeine doses, but this study provides no evidence that caffeine causes lower reaction times.
Correlation alone does not prove causation, but this scenario provides more evidence than just correlation between two variables.
Question
True or false: The larger the truck, the larger the load it can fit.
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Correct! You nailed it.
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True
False
Answer Explanation
Correct answer:
True
Increasing the truck's size will increase the size of the storage area, resulting in the truck fitting a larger load.
Question
An observational study shows a moderate negative correlation between the price of the car a person owns and the happiness of that person. Answer the following question based only on this information.
True or false: It can be concluded that in general, owning a more expensive car makes people less happy.
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Yes that's right. Keep it up!
________________________________________
True
False
Answer Explanation
Correct answer:
False
Correlation does not prove causation. The provided information shows that there is a negative association between the price of the car a person owns and the happiness of that person, but that information alone is not sufficient to conclude that owning a more expensive car causes people to be less happy. There could be a third variable associated with owning a more expensive car that causes people to be less happy. For example, it could be that people who choose to buy more expensive cars work harder or longer hours and that this is what causes them to be less happy
Question
True or False: The larger the number of cavities, the older the person.
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Well done! You got it right.
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True
False
Answer Explanation
Correct answer:
False
Changing the number of cavities will not affect the age of a person.
Question
True or false: Increases in height cause increases in shoe size.
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Well done! You got it right.
________________________________________
True
False
Answer Explanation
Correct answer:
False
Although a correlation between the values can be assumed, assuming that an increase in height causes an increase in shoe size is incorrect. A growth spurt could cause one value or the other to increase without causing both to change. A clearer example may be surgeries that affect height, as it can easily be seen that the height changes with no effect on shoe size. The correlation could be caused by genetic or hormonal factors that affect both, but this correlation does not imply causation.
Question
Suppose that data collected from police reports of motor vehicle crashes show a moderate positive correlation between the speed of the motor vehicle at the time of the crash and the severity of injuries to the driver. Answer the following question based only on this information.
True or false: It can be concluded that the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are.
________________________________________
Well done! You got it right.
________________________________________
True
False
Answer Explanation
Correct answer:
False
Correlation does not prove causation. The provided information shows that there is a positive association between speed and severity of injuries, but that information alone is not sufficient to conclude that greater speed causes more severe injuries. Based only on this information, there could be a third variable associated with speed that causes more severe injuries in crashes.
That said, the statement "the faster a motor vehicle is traveling at the time of a crash, the more severe the injuries to the driver are" does not imply a causal relationship between speed and severity of injuries. [Show Less]