# Statistics Problem Set: U.S. Energy Information

See the attachment.

14.6 What follows is Excel out put from a regression model to predict y using x1, x2, x1^2, x2^2, and the interaction term, x1,x2. Comment on the overall strength of the model and the significance of each predictor. The data follow the Excel output. Develop a regression model with the same independent variables as the first model but without the interaction variable. Compare this model to the model with interaction.

14.10 Given here is Excel output for a multiple regression model that was developed to predict y from two independent variable, x1 and x2. Variable x2 is a dummy variable. Discuss the strength of the multiple regression model on the basis of the output. Focus on the contribution of the dummy variable. Plot x1 and y with x2 and 0, and then plot x1 and y with x2 as 1. Compare the two lines and discuss the differences.

14.18 The U.S. Energy Information Administration releases figures in their publication, Monthly Energy Review, about the cost of various fuels and electricity. Shown here are the figures for four different items over a 12-year period. Use the data and step-wise regression to predict the cost of residential electricity from the cost of residential natural gas, residual fuel oil, and leaded regular gasoline. Examine the data and discuss the output.

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#### Solution Preview

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14.6 From the output, we could see that 91% of the total variation in the y could be explained by x1, x2, x1^2, x2^2 and the interaction term x1*x2. Therefore, Overall the regression model is a good one. However, for p values of coefficients of x1, x2, they are 0.1021 and 0.5471 respectively and both of them are larger than 0.05. Therefore, x1 and x2 could not significantly predict values of y. Meanwhile, for p values of coefficient of x1^2 and x^2, they are 0.0876 and 0.9394 and both of them are larger than 0.05. Therefore, x1^2 and x2^2 could not significantly predict values of y. However, for the interaction ...

#### Solution Summary

The solution discusses the United States energy information in the statistics problem.