We expect a car's highway gas mileage to be related to its city gas mileage (in miles per gallon, mpg). data for all 1137 vehicles in the government's 2013 fuel economy guide give the regression linehighway mpg = 6.785 + (1.033 × city mpg)for predicting highway mileage from city mileage.(a) what is the slope of this line? (enter your answer to three decimal in words what the numerical value of the slope tells us. a. on the average, highway mileage decreases by 1.033 mpg for each additional mpg in city mileage. b. highway gas mileage increases with city gas mileage by 6.785 mpg for each additional mpg in city mileage. c. on the average, highway mileage increases by 6.785 mpg for each additional mpg in city mileaged. for every 6.785 mpg in city gas mileage, highway gas mileage increases about 1.033 mpg. e. on the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage.(b) what is the intercept? (enter your answer to three decimal places.)mpgexplain why the value of the intercept is not statistically meaningful. a. because this is an average value, calculated from a sample. b. because this is the highway mileage for zero city mpg.
c. because this is the highway mileage for slope 0.(c) find the predicted highway mileage for a car that gets 18 miles per gallon in the city. (round your answer to two decimal mpgfind the predicted highway mileage for a car that gets 25 miles per gallon in the city. (round your answer to two decimal mpg(d) draw a graph of the regression line for city mileages between 10 and 50 mpg. (be sure to show the scales for the x and y axes.)

a) As we can see on the equation given the slope os 1.033 since is the value next to the city mpg (independent variable)

And on this case since the value for the slope is positive the best interpretation is:

E. On the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage

Because we see the if we increase on 1 unit the city mpg then the highway mpg would increase 1.033

b) For this case as we can see in the model the free term correspond to 6.785 and that correspond to the intercept for this case.

And the best interpretation is given by:

B. Because this is the highway mileage for zero city mpg.

For this reason is not meaningful since we are not interested on 0 or negative city mpg.

c) highway mpg = 6.785 + (1.033 × 18)=25.38 mpg

highway mpg = 6.785 + (1.033 × 25)=32.61 mpg

d) See the figure attached.

Step-by-step explanation:

For this case we have the following linear model:

highway mpg = 6.785 + (1.033 × city mpg)

(a) What is the slope of this line? Say in words what the numerical value of the slope tells us.

As we can see on the equation given the slope os 1.033 since is the value next to the city mpg (independent variable)

And on this case since the value for the slope is positive the best interpretation is:

E. On the average, highway mileage increases by 1.033 mpg for each additional mpg in city mileage

Because we see the if we increase on 1 unit the city mpg then the highway mpg would increase 1.033

(b) What is the intercept? (Enter your answer to three decimal places.)mpgExplain why the value of the intercept is not statistically meaningful.

For this case as we can see in the model the free term correspond to 6.785 and that correspond to the intercept for this case.

And the best interpretation is given by:

B. Because this is the highway mileage for zero city mpg.

For this reason is not meaningful since we are not interested on 0 or negative city mpg.

(c) Find the predicted highway mileage for a car that gets 18 miles per gallon in the city. (Round your answer to two decimal places.)______ mpgFind the predicted highway mileage for a car that gets 25 miles per gallon in the city. (Round your answer to two decimal places.)______ mpg

For this case we just need to replace into the formula and we got:

highway mpg = 6.785 + (1.033 × 18)=25.38 mpg

highway mpg = 6.785 + (1.033 × 25)=32.61 mpg

(d) Draw a graph of the regression line for city mileages between 10 and 50 mpg. (Be sure to show the scales for the x and y axes.)

See the figure attached

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.