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Indicator variables: indicate how much variation exists in a multiple regression

ID: 3256376 • Letter: I

Question

Indicator variables:

indicate how much variation exists in a multiple regression model.

allow nominal variables to be used in a regression model.

create multicollinearity within a model.

can take on any value between 0 and 5.

A multiple regression model has the form    y = 7 + 6 x1 + 3 x2      As x1 increases by 1 unit (holding x2 constant), y is expected to:

decrease by 3 units.

increase by 6 units.

decrease by 6 units.

increase by 3 units.

The residuals represent:

the difference between the actual Y values and the mean of Y.

the difference between the actual Y values and the predicted Y values.

the predicted value of Y for the average X value.

the square root of the slope.

a.

indicate how much variation exists in a multiple regression model.

b.

allow nominal variables to be used in a regression model.

c.

create multicollinearity within a model.

d.

can take on any value between 0 and 5.

Explanation / Answer

Indicator variables:

b. allow nominal variables to be used in a regression model.

Nominal variables are categorical variables such as Gender(Male, Female); Opinion(Good, Moderate, Bad) etc.. These variables cannot be used in a regression model as such as they are not numarical values. So we convert them into numerical values by assigning values 0, 1 2 etc to them. This allows it to be used as numerical values in regression.

A multiple regression model has the form    y = 7 + 6 x1 + 3 x2      As x1 increases by 1 unit (holding x2 constant), y is expected to:

b. increase by 6 units.

This is beacuse the x1 has a positive coefficient of 6. So any subsequent increase in x1 will only increase the value of y (as the coefficient sign is positive). The magnitude by which this increase happens in 6 as we hold x2 a constant.

The residuals represent:

b. the difference between the actual Y values and the predicted Y values.

The residuals is the difference between the actual Y values and the values of Y which is predicted by the fitted model. It helps us to get an idea about how large the difference is between the actual and predicted value.