Ask Question
16 December, 09:56

Accident rate data y1, ..., y12 were collected over 12 consecutive years t=1,2, ... 12. At over 12 consecutive years t = 1,2, ..., 12. At the end of the 6th year, a change in safety regulations occured. FOr each of the following situations, set up a linear model of the form y=XB+E. Define X and B appropriately.

a. The accident rate y is a linear function of t with the new safety regulations having no effect.

b. The accident rate y is a quadratic function of t with the new regulations having no effect.

c. The accident rate y is a linear function of t. The slope for t> = 7 is the same as for t<7. However there is a discrete jump for t=7.

d. The accident rate y is a linear function of t. After t=7, the slope changes, with the two lines intersecting at t=7.

+1
Answers (1)
  1. 16 December, 10:10
    0
    The correct option is;

    The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7

    Step-by-step explanation:

    The given parameters are;

    Accident rate data = y₁, y₂, y₃, y₄, y₅, y₆, y₇, y₈, y₉, y₁₀, y₁₁, y₁₂

    Time at which data was recorded = t₁, t₂, t₃, t₄, t₅, t₆, t₇, t₈, t₉, t₁₀, t₁₁, t₁₂

    Accident rate equation is a linear model given as follows;

    y = X·B + E

    Where:

    y = Accident rate

    X = Slope of linear model

    B = Year

    E = y intercept of model

    At the end of the 6th year, a change in a regulation that affects safety, hence accident rate occurred given as follows;

    Before the change in safety regulations occurred for year t < 7 y₁ = X₁B + E₁

    After the change in safety regulations occurred for year t < 7 y₂ = X₂B + E₂

    Therefore the slope changes from X₁ to X₂ after t = 7 with the second linear model starting from the end of the first linear model making the two lines intersect at t = 7 (the beginning of year 7)

    Hence the correct option is that "The accident rate is a linear model function of t. After t = 7, the slope changes, with the two lines intersecting at t = 7."
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Accident rate data y1, ..., y12 were collected over 12 consecutive years t=1,2, ... 12. At over 12 consecutive years t = 1,2, ..., 12. At ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers