Non Linear Data and Residuals

Shown is a residual plot. How many positive residuals are there?

• 5

• 1

• 3

• 9

Which best describes the scatterplot?

• linear; positive correlation

• linear; negative correlation

• non-linear; negative correlation

• non-linear; positive correlation

A negative residual means...

• that the predicted value is too big

• that the predicted value is too small

• that the x value is too big

• that the x value is too small

What is the best function type to model this data set?

• Linear function.

• Exponential function.

• Quadratic function.

• Cubic function.

Answer explanation

Linear function is of the form y=a+bx. Exponential function is of the form y = Ae^kx. A quadratic function is of the form y =ax²+bx+c and this is a parabola that has an axis of symmetry passing through its vertex. This is the shape best to model this data. A cubic has the form y=ax³+bx²+cx+d.

• A

• B

• C

• D

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Question 27

• 1

• 2

• 3

• 4

Shown is a residual plot. How many negative residuals are there?

• 5

• 1

• 3

• 9

Question 9

• 1

• 2

• 3

• 4

• The equation is a good fit because the residual points have a positive association

• The equation is a good fit because the residual points are approximately linear

• The equation is not a good fit because the residual plot with the pattern from the data set indicates a bad fit

• The equation is not a good fit because there should be an equal number of points below and above the x-axis in the residual plot