5. Suppose you believe that a continuous response variable Y and a continuous pr

Question

5. Suppose you believe that a continuous response variable Y and a continuous predictor variable X are related as shown in the figure below. That is, Y increases linearly with X, but a change in slope may occur at a known change point X = 20. (a) How would you fit this model? State the model equation and explain. (b) How would you test the nul hypothesis that the slopes over the two regions X S ro and X>o are equal? (c) How would you test the null hypothesis that E(YX-ro) = 5? Hint: When you write the equation of the model, you have a multiple linear regression model. We have different tests for different hypotheses. For example, for part (b), the slope will be the same, if you just have a simple linear model, that is, if one of the coefficients is zero. That is a t test or equivalently an F test. For part (c), remember the general F test.

Explanation / Answer

A. The model given is the reduced model as per it the null hypothesissets each of parameter in the full model equation to 0. The reduced model equation is yi=B0+e1

B.

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