Question

Let us imagine that the number of automobile accidents in a certain region are related to the regional number of registered automobiles in tens of thousands (b1), alcoholic beverage sales in $10,000 (b2), and decrease in the price of gasoline in cents (b3). Furthermore, imagine that the regression formula has been calculated as: Y = a + b1X1 + b2X2 + b3X3 where Y = the number of automobile accidents, a = 7.5, b1 = 3.5, b2 = 4.5, and b3 = 2.5 Calculate the expected number of automobile accidents for a football weekend if the region has 25,000 registered vehicles, $75,000 worth of beer is sold, and a gas war causes a 10 cent drop in a gallon of gas.

Answer 1

75 accidents

Explanation:

Given:

a = 7.5

b1 = 3.5

b2 = 4.5

b3 = 2.5

Given that the number of automobile accidents in a certain region are related to the regional number of registered automobiles in tens of thousands(10,000) and alcoholic beverage sales in $10,000, let's divide X1 and X2 by 10,000

X1 = 25,000
`= (25,000)/(10,000) = 2.5`

X2 = 75,000
`= (75,000)/(10,000) = 7.5`

X3 = 10

We are to imagine the regression formula has been calculated as:

Y = a + b1X1 + b2X2 + b3X3

Let's substitute the given figures in the formula,

`Y = 7.5 + (3.5*2.5) + (4.5*7.5) + (2.5*10)`

Y = 7.5 + 8.75 + 33.75 + 25

Y = 75

Therefore, the expected number of automobile accidents for a football weekend given the above conditions are 75 accidents.