Chapter PII, Problem 39RE

(a)

To determine

To estimate the weight of a truck if this scale read $31200$ pounds.

Answer to Problem 39RE

  $30818$ pounds is the predicted weight.

Explanation of Solution

It is given in the question that the Minnesota department of transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weigh-in-motion scale. Their regression equation is:

  

where both the scale reading and the predicted weight of the truck are measured in thousands of pounds.

Thus, we can estimate the weight of a truck if this scale read $31200$ pounds as:

  

Thus, $30818$ pounds is the predicted weight.

(b)

To determine

To find out what was the residual if that truck actually weighed $32120$ pounds.

Answer to Problem 39RE

The residual is $1302\text{ pounds}$ .

Explanation of Solution

It is given in the question that the Minnesota department of transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weigh-in-motion scale. Their regression equation is:

  

where both the scale reading and the predicted weight of the truck are measured in thousands of pounds.

Now, if that truck actually weighed $32120$ pounds and the predicted weight is $30818$ pounds then the residual is as:

  $\begin{array}{l}\text{Residual}=\text{Observed}-\text{Predicted}\\ =32120-30818\\ =1302\text{ pounds}\end{array}$

(c)

To determine

To explain how much does it actually weigh.

Answer to Problem 39RE

  $31187.6$ pounds.

Explanation of Solution

It is given in the question that the Minnesota department of transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weigh-in-motion scale. Their regression equation is:

  

where both the scale reading and the predicted weight of the truck are measured in thousands of pounds.

Now, if the scale reads $35590$ pounds and the truck has a residual of $-2440$ pounds then the actual weight is:

  

The actual weight is $31187.6$ pounds.

(d)

To determine

To explain do you expect estimates made using this equation to be reasonably accurate.

Answer to Problem 39RE

No, we do not expect.

Explanation of Solution

It is given in the question that the Minnesota department of transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weigh-in-motion scale. Their regression equation is:

  

where both the scale reading and the predicted weight of the truck are measured in thousands of pounds. Thus, we do not expect estimates made using this equation to be reasonably accurate because it is not extremely that a residual margin of error of $1000$ is not very accurate.

(e)

To determine

To explain will negative or positive residuals be a greater problem if the police plan to use this scale to issue tickets to trucks that appear to be overloaded.

Answer to Problem 39RE

Explanation of Solution

It is given in the question that the Minnesota department of transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed weigh-in-motion scale. Their regression equation is:

  

where both the scale reading and the predicted weight of the truck are measured in thousands of pounds. Thus, the negative residuals be a greater problem if the police plan to use this scale to issue tickets to trucks that appear to be overloaded because the predicted weight would be higher than the actual weight which could cause false tickets.