When a scatter chart of data shows a nonlinear relationship, the nonlinear model can be expressed as:
a) y = β0 + β1x + (β2x)2 + ε
b) y = β0 + β1x + β2x2 + ε
c) y = β0 + β1x + β2x
d) y = β0 + β1x2 + β2x2 + ε

A

Step-by-step explanation:

The linear model can be assessed by the checking the independent variables having power 1 which shows the linear relationship between x and y. For example, as in the option B, C and D, the power of Xi's is one. Whereas the non linear model has the power for independent variables greater than 1. For example, as in option  A the model is a quadratic model because X associated with β2 has a power of a 2.

Thus the nonlinear model can be expressed as

Y = β0 + β1X + (β2X)2 + ε.

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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the answer is b.)

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