Question

Your attention is directed to the lorry data.(Here is the data)

Moving    26 29.9 39.5 25.1 31.6 36.2 25.1 31   35.6 40.2

        Statics   27.9 29.1 38 27 30.3 34.5 27.8 29.6 33.1 35.5

We want to see if we can predict static weight by weighing the truck while it is in motion. (a)   Find the regression line expressing static weight as a function of moving weight. Be sure to use the proper notation for this equation. (b)   Find the slope and interpret in the context of the situation. (c)   Find the y-intercept and interpret it in the context of the situation.   (d)   Does the static weight given by the y-intercept make sense? Why or why not? (e)   Find the predicted value for the lorry that weighs 31,000 pounds in motion. (f)   Find the residual for 31,000-pound lorry and interpret this residual in context. (g)   Use the equation in (g) to predict the static weight of a minivan that weighs 6,000 pounds. (h)   Does the prediction made in (g) make sense? Why or why not?

Answer 1

Let Y=static weight of the truck (in thousand pounds)

x=moving weight of the truck (in thousand pounds)

The regression line that we want to estimate is

First we calculate the following

get these sum of squares

(a)   Find the regression line expressing static weight as a function of moving weight. Be sure to use the proper notation for this equation.

The estimate of slope is

An estimate of the intercept is

ans: The regression line expressing static weight as a function of moving weight is

where is the predicted static weight (in 1000s of pounds) and x is the moving weight

(b)   Find the slope and interpret in the context of the situation.

ans: The slope of the regression line is 0.6379. The positive value indicates that the moving weight and static weight move in the same direction. For example, for each 1000 pound increase in the moving weight, the predicted static weight increases by 637.91 pounds (which is 0.6379*1000)

(c)   Find the y-intercept and interpret it in the context of the situation.  

ans: the value of the y-intercept is 10.8540. This indicates that when the moving weight of the truck is 0 pounds, the static weight is predicted to be 10853.98 pounds

(d)   Does the static weight given by the y-intercept make sense? Why or why not?

The value of moving weight of the truck to be 0 pound does not make sense. Hence the predicted static weight at 0 pounds of moving weight is senseless.

(e)   Find the predicted value for the lorry that weighs 31,000 pounds in motion.

The predicted value of Y for x=31 (thousand pounds) is

ans: the predicted value for the lorry that weighs 31,000 pounds in motion is 30629.33 pounds

(f)   Find the residual for 31,000-pound lorry and interpret this residual in context.

The actual static weight when the moving weight is 31 (thousand pounds) is 29.6 (thousand pounds)--from the sample data.

The residual is

Ans: The residual is -1.0293. This indicates that the regression line over estimates the static weight by 1029.33 pounds, for 31,000-pound lorry.

(g)   Use the equation in (g) to predict the static weight of a minivan that weighs 6,000 pounds.

The predicted value of Y for x=6 (thousand pounds) is

ans: The predicted the static weight of a minivan that weighs 6,000 pounds (while moving ) is 14681.47 pounds

(h)   Does the prediction made in (g) make sense? Why or why not?

The minimum value of moving weight (value of x) in the sample is 25.1 and the maximum value is 40.2. We are not sure if the linear regression line is valid outside this range. We are trying to predict for x=6. This is very much outside the sample range 25.1 to 40.2. Hence the prediction made in g) does not make sense.