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A linear model has the following characteristics:
"¢ A dependent variable (y)
"¢ One continuous variable (x1)
"¢ One categorical (Ñ1 with 3 levels) predictor variable and an interaction term (Ñ1 by x1)
How many parameters, including the intercept, will be estimated for this model?
Enter your numeric answer in the space below.
To determine the number of parameters in a linear model with the given characteristics, we need to account for each component: the intercept, the continuous variable, the categorical variable with 3 levels, and the interaction term. The intercept contributes 1 parameter. The continuous variable (x1) contributes 1 parameter. The categorical variable with 3 levels contributes 2 parameters (since we need k-1 parameters for k levels). The interaction term (Ñ1 by x1) between the categorical variable (Ñ1 with 3 levels) and the continuous variable (x1) contributes 2 parameters (one for each interaction level). Adding these together, we have 1 (intercept) + 1 (x1) + 2 (Ñ1) + 2 (interaction) = 6 parameters to be estimated.
I think this is wrong. Original question had a "quadratic" variable and this question excludes it and should be 6, not 7
intercept = 1 "¢ A dependent variable (y) = 1 "¢ One continuous variable (x1) = 1 "¢ One categorical (Ñ1 with 3 levels) predictor variable = 2 interaction term (Ñ1 by x1) = 2 Total of 7 parameters
I also think that it is 6