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week11 - Rainfall Example The data set contains cord...

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STA302/1001 - week 11 1 Rainfall Example The data set contains cord yield (bushes per acre) and rainfall (inches) in six US corn-producing states (Iowa, Nebraska, Illinois, Indiana, Missouri and Ohio). Straight line model is not adequate – up to 12″ rainfall yield increases and then starts to decrease. A better model for this data is a quadratic model: Yield = β 0 + β 1 ∙rain + β 2 ∙rain 2 + ε. This is still a multiple linear regression model since it is linear in the β’s. However, we can not interpret individual coefficients, since we can’t change one variable while holding the other constant…
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STA302/1001 - week 11 2 More on Rainfall Example Examination of residuals (from quadratic model) versus year showed that perhaps there is a pattern of an increase over time. Fit a model with year… To assess whether yield’s relationship with rainfall depends on year we include an interaction term in the model…
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STA302/1001 - week 11 3 Interaction Two predictor variables are said to interact if the effect that one of them has on the response depends on the value of the other. To include interaction term in a model we simply the have to take the product of the two predictor variables and include the resulting variable in the model and an additional predictor. Interaction terms should not routinely be added to the model. Why? We should add interaction terms when the question of interest has to do with interaction or we suspect interaction exists (e.g., from plot of residuals versus interaction term).
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