Question

We have a negative relationship between number of drinks consumed and number of marks in a driving test. One individual scores 3 on number of drinks consumed, another individual scores 5 on number of drinks consumed. What will be their respective scores on the driving test if the intercept is 18 and the slope -3? A. Driving test scores (y-axis) will be 27 [individual who scored 3 on drink consumption and 33 [individual who scored 5 on drink consumption]. B. It is not possible to predict from negative relationships. C. Driving test scores (y-axis) will be 9 [individual who scored 3 on drink consumption and 3 [individual who scored 5 on drink consumption]. D. Driving test scores (y-axis) will be 51 and 87 [individual who scored 5 on drink consumption].

Answer 1

C. Driving test scores (y-axis) will be 9 [individual who scored 3 on drink consumption and 3 [individual who scored 5 on drink consumption].

Correct as we can see:

`y(3) =-3(3) +18 = -9 +18 =9`

`y(5) =-3(5) +18 = -15 +18 =3`

Explanation:

Let's define some notation:

y= represent the driving test scores

x= represent the number of drinks consumed

We know this info given: "What will be their respective scores on the driving test if the intercept is 18 and the slope -3?" So then we can create the following linear model:

`y = -3x +18`

And now we have two values for x we can replace and see what we got:

`y(3) =-3(3) +18 = -9 +18 =9`

`y(5) =-3(5) +18 = -15 +18 =3`

And if we analyze one by one the options we got this:

A. Driving test scores (y-axis) will be 27 [individual who scored 3 on drink consumption and 33 [individual who scored 5 on drink consumption].

False.

`y(3) =-3(3) +18 = -9 +18 =9`

`y(5) =-3(5) +18 = -15 +18 =3`

B. It is not possible to predict from negative relationships.

False, we have the linear model given and we can find the predicted values.

C. Driving test scores (y-axis) will be 9 [individual who scored 3 on drink consumption and 3 [individual who scored 5 on drink consumption].

Correct as we can see before:

`y(3) =-3(3) +18 = -9 +18 =9`

`y(5) =-3(5) +18 = -15 +18 =3`

D. Driving test scores (y-axis) will be 51 and 87 [individual who scored 5 on drink consumption].

False.