1. Which of the following statements about linear regression models is false?
a. If r = -1, the linear model fits the data perfectly and the graph of the model is a decreasing line.
b. If r^2 = -1, the linear model fits the data perfectly and the graph of the model is decreasing line
c. If r = 0, the linear model does not fit the data well.
d. The linear regression model fits the data perfectly and is the linear model with the same number as sum of squares
2. Which of the following will result in a dependent system of linear equations?
a. A system of two linear equations whose graphs are identical
b. A system of three linear equations whose graphs have different slopes.
c. A system of two linear equations whose graphs are parallel.
d. A system of three linear equations whose graphs don't intersect in a common point
a. If r = -1, the linear model fits the data perfectly and the graph of the model is a decreasing line.
b. If r^2 = -1, the linear model fits the data perfectly and the graph of the model is decreasing line
c. If r = 0, the linear model does not fit the data well.
d. The linear regression model fits the data perfectly and is the linear model with the same number as sum of squares
2. Which of the following will result in a dependent system of linear equations?
a. A system of two linear equations whose graphs are identical
b. A system of three linear equations whose graphs have different slopes.
c. A system of two linear equations whose graphs are parallel.
d. A system of three linear equations whose graphs don't intersect in a common point
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Question 1: B
r^2, also known as the coefficient of determination is basically a tool telling you the "goodness of fit" of your regression model. Further more, -=< r <= 1. so r^2 >=0 for any r in that interval.
Question 2: A
If two equations have identical graphs, then one is simply a scalar multiple of the other. So the homogeneous system will contain more than the trivial solution and thus, by definition of dependence, the system is linearly dependent.
r^2, also known as the coefficient of determination is basically a tool telling you the "goodness of fit" of your regression model. Further more, -=< r <= 1. so r^2 >=0 for any r in that interval.
Question 2: A
If two equations have identical graphs, then one is simply a scalar multiple of the other. So the homogeneous system will contain more than the trivial solution and thus, by definition of dependence, the system is linearly dependent.