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# econ103ps4answers - Problem Set 4 Economics 103 Spring 2008...

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6) In the following polynomial regression model Y i = 100 + 5.4 X i - 0.1 X i 2 the relationship between X i and Y i is concave (you can answer this either with or without calculus). True. Using Calculus, the derivative of this function is 5.4 – 0.2 X i , and the second derivative is -0.2. Since the second derivative is negative, the function is concave. One can also do this by plugging in various values of X i . When X i = 1, Y i = 105.3, when X i = 2, Y i = 110.4, and when X i = 3, Y i = 115.3. Since the effect of increasing X i by one unit decreases as X i increases, the function is concave (you could also plot these points and see that the function looks concave (the function looks like a cave when viewed from below). Longer Answer:
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econ103ps4answers - Problem Set 4 Economics 103 Spring 2008...

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