Statistics help Data on 147 cars were obtained from the October 2002 issue of Ro

Question

Statistics help

Data on 147 cars were obtained from the October 2002 issue of Road& Track: The New Cars. The following variables were available in order to predict selling price (y): (Hint: Realize that the raw data are not necessary in order to answer these questions and therefore are NOT provided in the HW11 Data file.) weight, in pounds (WEIGHT) mileage in city driving (CITYMPG) mileage in highway driving (HWYMPG) horsepower,@ 6300 rpm (HP) number of cylinders (CYLIN) displacement, in liters (LITER) (a) If an all possible regressions analysis is performed, how many regression models are possible? (Enter a whole number.) (b) For the number of models you found above, which of the following statements are true? (Select all that apply.) [ ] This includes a model with no explanatory variables and only the intercept (i.e., the mean model) This does not include a model with no explanatory variables (i.e., the mean model). This does not include 1 model with all explanatory variables. This includes 1 model with all explanatory variables This includes 6 1-variable models. This does not include 6 1-variable models.

Explanation / Answer

(a) The number of possible models that can be formed from p regressors is 2 to the power p.

Here, since we have 6 regressor variables, number of regression models possible are : 26 = 64

(b) Possible regression equation combinations:

Set 1: Y = 0 + (1 model with only intercept)

Set 2: Y = 0 + i Xi + , i = 1,2,3,4,5,6 (6 -1 variable models)

Set 3: Y = 0 + 1X1 + 2 X 2 + 3X3 + 4 X 4 + 5 X 5 + 6 X 6 + (1 model with all the variables)

and other combinations.

True statements are:

1. This includes a model with no explanatory variables and only the intercept.

4. This includes a model with all explanatory variables.

5. This includes 6 -1 variable models.

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