SIMULATION -
A linear model has the following characteristics:
*A dependent variable (y)
*One continuous variable (xl), including a quadratic term (x12)
*One categorical (d with 3 levels) predictor variable and an interaction term (d by x1)
How many parameters, including the intercept, are associated with this model?
Enter your numeric answer in the space below. Do not add leading or trailing spaces to your answer.
To determine the number of parameters in this linear model, consider each part of the model individually. There is one continuous variable (x1), which also includes a quadratic term (x1^2). Then, there is one categorical variable (d) with 3 levels. Since the model uses categorical variables, the number of parameters for d will be the number of levels minus 1, which is 2 parameters (one for each level beyond the reference level). Additionally, there are interaction terms between the categorical variable and the continuous variable. This leads to 2 more parameters (each of the two levels interacts with x1). Summarizing, we have: one intercept, one x1, one x1^2, two for the levels of d, and two for the interaction terms. This totals to 7 parameters.
please explain how it is 7
these are the predictors: [x1 , x1^2, b2, b3, x1*b2, x1*b3 , 1] 7 columns, 7 coefficients
Simpler explanation: 1 continuous variable, 1 quadratic term, 3 levels - 1= so 2 levels = 2, 1 level + interaction effect = 1 1 level(other level) + interaction effect =1 1 intercept =7 total