In this section you started working with bivariate data: data for two variables collected on each object.
In this section you started working with bivariate data: data for two variables collected on each object.
• What is the name of the graph that we use to look at the relation between two quantitative variables?
• What is the formula for the linear regression equation? __________________________________
• Why is there a “hat” on top of the Y in the equation above
• What is the restricted domain for the linear regression equation?
• What is the formula to compute a residual?
How can you use your TI84 to find predicted values of Y?
• What is the general wording of how to interpret a slope?
• What is the general wording of how to interpret the Y-intercept?
• Why on some problems does it not make sense to interpret the Y-Intercept?
Remember for bigger data sets you can copy and paste the columns of data into StatCrunch.
For smaller sets of data you should practice using your TI84 since that is the only technology you have available in the classroom when you take the departmental final exam.
Fill in the following as you work through your given problems in MyOpenMath
1.
a) State the random variables.
b) Make a scatterplot of X versus Y in StatCrunchor on your TI84. Make a quick sketch below.
Find the equation of the best-fitting line (the least squares regression equation). Include the restricted domain.
c) Interpret the slope in the context of this problem. (Pay attention to the units)
d) Interpret the Y-intercept in the context of this problem or state why it does not make sense to do so.
When length of metacarpal is 0 cm, we expect the height to be 105.97 cm
e) Should you use the regression equation to predict the ___ _______of a randomly selected _set of skeletal remains _______ ____ _______ ________ _cm_____? __yes, this X-value is between Xmin and Xmax ________________
Should you use the regression equation to predict the __ ________of a randomly selected __set of skeletal remains ______ that has a __length_________ of ___ ___ __ ______? ________no, this X-value is not between Xmin and Xmax __________
Predict the _height___________ for the one above that it made sense to do so.
The predicted _height_____________ for a randomly selected ____set of skeletal remains __________ that has a ___ ________ of __________ __cm_____ is ______________ _cm_______
f) Compute the residual for the following ordered pair in the data: __(44,173)_________________
o The residual for the ___ _________ ____________ of _____ ___ _cm____ is __ ___________ _cm_____________
Interpret what this value means in the context of this problem.
o The actual ___ __________ of a randomly selected _set of skeletal remians____________ with a __length ___________ ___ __________________ is_____________ ____________________ what was predicte
2.
a) State the random variables.
rv X = the weight of a randomly selected car
rv Y = the mileage of a randomly selected car
b) Make a scatterplot of X versus Y in StatCrunch or on your TI84. Make a quick sketch below.
c) Find the equation of the best-fitting line (the least squares regression equation). Include the restricted domain.
Y? = 71.748 + -0.012 *X
restricted domain: 2250 pounds <= X <= 4500 pounds.
d) Interpret the slope in the context of this problem. (Pay attention to the units)
Every time we increase the weight by 1 pound we can expect the mileage to decrease by 0.012 mpg on average.
e) Interpret the Y-intercept in the context of this problem or state why it does not make sense to do so.
When weight is 0 pounds , we expect the mileage to be 71.748 mpg.
Does it make sense to interpret the Y-intercept on this problem? _no___ Why or why not? since X = 0 is not between Xmin and Xmax
f) Should you use the regression equation to predict the ___ _______of a randomly selected _____car___ that has a ___weight________ of ___ _____ ______? __ ,
Should you use the regression equation to predict the ____ ______of a randomly selected _____car___ that has a ___weight________ of ________ ______? __ ________________
Predict the ________mileage____ for the one above that it made sense to do so.
The predicted ___mileage___________ for a randomly selected __car____________ that has a ____weight_______ of __________ __pounds_____ is ___________ _mpg_______
g) Compute the residual for the following ordered pair in the data: ________________
o The residual for the ___car__________ with a __weight___________ of __4000______ _pounds____ is ___-__________ ____mpg__________
Interpret what this value means in the context of this problem.
o The actual ______mileage_______ of a randomly selected __car___________ with a _________weight____ of ____ _________________ is ______________________ below___________ what was predicted.
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