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There are six independent variables, x1, x2, x3, x4, x5,
Chapter 12, Problem 111E(choose chapter or problem)
There are six independent variables, \(x_1\), \(x_2\), \(x_3\), \(x_4\), \(x_5\), and \(x_6\), that might be useful in predicting a response y. A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The softwarefits all possible one-variable models of the form
\(E(y)=\beta_0+\beta_1x_1\)
where \(x_i\) is the ith independent variable, i = 1, 2,... , 6.The information in the table is provided from the computer printout.
a. Which independent variable is declared the best one-variable predictor of y? Explain.
b. Would this variable be included in the model at this stage? Explain.
c. Describe the next phase that a stepwise procedure would execute.
Questions & Answers
QUESTION:
There are six independent variables, \(x_1\), \(x_2\), \(x_3\), \(x_4\), \(x_5\), and \(x_6\), that might be useful in predicting a response y. A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The softwarefits all possible one-variable models of the form
\(E(y)=\beta_0+\beta_1x_1\)
where \(x_i\) is the ith independent variable, i = 1, 2,... , 6.The information in the table is provided from the computer printout.
a. Which independent variable is declared the best one-variable predictor of y? Explain.
b. Would this variable be included in the model at this stage? Explain.
c. Describe the next phase that a stepwise procedure would execute.
ANSWER:Step 1 of 3
(a) Finding t - test for all the 6 independent variable among all of them highest is the
best variable for prediction (y).
By de?nition,
The t-value for the independent variables is shown in below.
Therefore, 
variable predictor of y.