Final answer:
In the population model 'yi = β₀ + β₁x + ε', the βj are parameters, which are constants that define the linear relationship between variables in a statistical model. The estimates of these parameters obtained from sample data are called statistics. The correct answer is option b. statistics.
Step-by-step explanation:
In the context of the population model yᵢ = β₀ + β₁x + ε, the βj (where j can be 0,1,..,n for different coefficients) are parameters of the model. Parameters are values that define the relationship between variables in a statistical model and remain constant within the context of that model. They are not directly observable in the data but are estimated through statistical methods.
In a population regression line, we assume there is a linear relationship, where the average value of y for different values of x can be modeled. When we collect data and calculate a regression line from that data, the slope b and intercept a are the estimates for the population parameters ß (slope) and α (intercept). The least-squares regression line estimates these parameters using sample data. The estimated slope and intercept are called statistics since they come from sample data and serve to estimate the true population parameters.
Using these estimators, we can also attempt to estimate the population standard deviation of the y-values. Here we use the standard deviation of the residuals s, calculated as s = √(SSE/n-2) where SSE is the sum of the squared errors, and n is the number of observations in the sample. The standard deviation of the residuals provides an estimate for the standard deviation of the y-values around the regression line.