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.

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."

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: