Reading Questions 25

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Problem 1. 

True or false: Linear regression can be used to fit a parabola to data.

 True
 False
  

Problem 2. 

In the least squares model y=a+bx the variable x is called:

 the ordinate
 the dependendent variable
 the predictor variable
 the confounding variable
  

Problem 3. 

Lollipop Kids

Consider the sample space of children under 13 in the United States. The random variable X represents the age of a child. The random variable Y represents the number of lollipops possessed by the child. By catching and releasing three children, we record the sample data:

      (1,2), (2,3), (3,3)

of the form (x,y).

(a) Calculate the sample means for the x data and the y.

(a.i) Mean for x:
 

(a.ii) Mean for y:
 

(b) Using least squares determine the best-fit line in the xy-plane: a+bx

(b.i) Give a.
 

(b.ii) Give b.
 

Problem 4. 

We use simple linear regression to predict the skill level of NBA players' sons from the skill level of their fathers. According to the prediction how will the sons compare with their fathers? On average they are:

 Worse
 Better
 The same
 No way to tell